"uuid","repository link","title","author","contributor","publication year","abstract","subject topic","language","publication type","publisher","isbn","issn","patent","patent status","bibliographic note","access restriction","embargo date","faculty","department","research group","programme","project","coordinates"
"uuid:2f279dff-0ea2-4987-a0da-63d0c1df0be5","http://resolver.tudelft.nl/uuid:2f279dff-0ea2-4987-a0da-63d0c1df0be5","Algebraic multiscale grid coarsening using unsupervised machine learning for subsurface flow simulation","Ramesh Kumar, K. (TU Delft Reservoir Engineering); Tene, Matei (SLB Norway Technology Center)","","2023","Subsurface flow simulation is vital for many geoscience applications, including geoenergy extraction and gas (energy) storage. Reservoirs are often highly heterogeneous and naturally fractured. Therefore, scalable simulation strategies are crucial to enable efficient and reliable operational strategies. One of these scalable methods, which has also been recently deployed in commercial reservoir simulators, is algebraic multiscale (AMS) solvers. AMS, like all multilevel schemes, is found to be highly sensitive to the types (geometries and size) of coarse grids and local basis functions. Commercial simulators benefit from a graph-based partitioner; e.g., METIS to generate the multiscale coarse grids. METIS minimizes the amount of interfaces between coarse partitions, while keeping them of similar size which may not be the requirement to create a coarse grid. In this work, we employ a novel approach to generate the multiscale coarse grids, using unsupervised learning methods which is based on optimizing different parameter. We specifically use the Louvain algorithm and Multi-level Markov clustering. The Louvain algorithm optimizes modularity, a measure of the strength of network division while Markov clustering simulates random walks between the cells to find clusters. It is found that the AMS performance is improved when compared with the existing METIS-based partitioner on several field-scale test cases. This development has the potential to enable reservoir engineers to run ensembles of thousands of detailed models at a much faster rate.","Algebraic multiscale methods; Computational performance; Graph-based partitioning; Reservoir simulation; Unsupervised learning","en","journal article","","","","","","","","","","","Reservoir Engineering","","",""
"uuid:966faa2d-f51c-4ded-acd8-6a0c3ecf3dc0","http://resolver.tudelft.nl/uuid:966faa2d-f51c-4ded-acd8-6a0c3ecf3dc0","Fully-Coupled Multiscale Poromechanical Simulation Relevant for Underground Gas Storage","Ramesh Kumar, K. (TU Delft Reservoir Engineering); Tasinafo Honório, H. (TU Delft Reservoir Engineering); Hajibeygi, H. (TU Delft Reservoir Engineering)","Barla, Marco (editor); Insana, Alessandra (editor); Di Donna, Alice (editor); Sterpi, Donatella (editor)","2023","Successful transition to renewable energy supply depends on the development of cost-effective large-scale energy storage technologies. Renewable energy can be converted to (or produced directly in the form of) green gases, such as hydrogen. Subsurface formations offer feasible solutions to store large-scale compressed hydrogen. These reservoirs act as seasonal storage or buffer to guarantee a reliable supply of green energy in the network. The vital ingredients that need to be considered for safe and efficient underground hydrogen storage include reliable estimations of the in-situ state of the stress, especially to avoid failure, induced seismicity and surface subsidence (or uplift). Geological formations are often highly heterogeneous over their large (km) length scales, and entail complex nonlinear rock deformation physics, especially under cyclic loading. We develop a multiscale simulation strategy to address these challenges and allow for efficient, yet accurate, simulation of nonlinear elastoplastic deformation of rocks under cyclic loading. A coarse-scale system is constructed for the given fine-scale detailed nonlinear deformation model. The multiscale method is developed algebraically to allow for convenient uncertainty quantifications and sensitivity analyses.","Algebraic multiscale method; Energy storage; Inelasticity; Poromechanics","en","conference paper","Springer","","","","","Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.","","2023-07-01","","","Reservoir Engineering","","",""
"uuid:b0ac2c6d-c005-4b22-aaaa-a04ad9753323","http://resolver.tudelft.nl/uuid:b0ac2c6d-c005-4b22-aaaa-a04ad9753323","Advancing Artificial Neural Network Parameterization for Atmospheric Turbulence Using a Variational Multiscale Model","Janssens, M. (Wageningen University & Research); Hulshoff, S.J. (TU Delft Aerodynamics)","","2022","Data-driven parameterizations offer considerable potential for improving the fidelity of General Circulation Models. However, ensuring that these remain consistent with the governing equations while still producing stable simulations remains a challenge. In this paper, we propose a combined Variational-Multiscale (VMS) Artificial Neural Network (ANN) discretization which makes no a priori assumptions on the model form, and is only restricted in its accuracy by the precision of the ANN. Using a simplified problem, we demonstrate that good predictions of the required closure terms can be obtained with relatively compact ANN architectures. We then turn our attention to the stability of the VMS-ANN discretization in the context of a single implicit time step. It is demonstrated that the ANN parameterization introduces nonphysical solutions to the governing equations that can significantly affect or prevent convergence. We show that enriching the training data with nonphysical states from intra-time step iterations is an effective remedy. This indicates that the lack of representative ANN-induced errors in our original, exact training inputs underpin the observed instabilities. In turn, this suggests that data set enrichment might aid in resolving instabilities that develop over several time steps.","Artificial Neural Networks; atmospheric boundary layer turbulence; machine learning; subgrid-scale modeling; variational multiscale methods","en","journal article","","","","","","","","","","","Aerodynamics","","",""
"uuid:434a324c-0ed4-4018-b57d-3384e39498ec","http://resolver.tudelft.nl/uuid:434a324c-0ed4-4018-b57d-3384e39498ec","Turbulent kinetic dissipation analysis for residual-based large eddy simulation of incompressible turbulent flow by variational multiscale method","Chen, Linfeng (Jiangsu University of Science and Technology); Hulshoff, S.J. (TU Delft Aerodynamics); Dong, Yuhong (Shanghai University)","","2022","The underlying physical mechanism of the residual-based large eddy simulation (LES) based on the variational multiscale (VMS) method is clarified. Resolved large-scale energy transportation equation is mathematically derived for turbulent kinetic energy budget analysis. Firstly, statistical results of benchmark turbulent channel flow at Reτ=180 obtained using a coarse mesh are compared with the results obtained by the classical LES with the Smagorinsky and dynamic subgrid stress (SGS) model. The present LES shows an advantage in predicting the statistical results of the incompressible turbulent flows. Secondly, the contributions of the unresolved small-scale presentation terms (Term I-IV in Eq. (10)) to the turbulent kinetic dissipation are analysed for the VMS method. The results show that the turbulent kinetic dissipation provided by the numerical diffusion in the VMS method is smaller in the inner layer, larger in the outer layer of the channel flow than those by the Smagorinsky and dynamic SGS model. The turbulent kinetic dissipation in the VMS method is mainly given by the numerical diffusion provided by one of the “cross-stress” terms (Term I, same as the stabilization term in the SUPG method) and LSIC term (Term IV). The other one of the “cross-stress” terms (Term II) gives rise to the positive turbulent kinetic energy budget, and does not dissipate the turbulent kinetic energy. The so-called “Reynolds stress” term (Term III) dissipates the turbulent energy but provides a very small numerical diffusion. Finally, on the basis of the turbulent kinetic energy dissipation analysis, a new residual-based stabilized finite element formulation is proposed by modifying the large-scale equation in the VMS method. Numerical experiments of 2D lid-driven cavity flow and 3D incompressible turbulent channel flow are tested to validate the proposed formulation. It is shown that all the stabilization terms in the proposed formulation produce additional numerical diffusions and physically increase the total turbulent kinetic dissipation. Consequently, an apparent improvement in both the first-order and second-order statistical quantities are pursued by the new stabilized finite element formulation.","Large-scale energy transportation; New stabilized finite element formulation; Residual-based large eddy simulation; Turbulent kinetic dissipation; Variational multiscale method","en","journal article","","","","","","Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.","","2023-07-01","","","Aerodynamics","","",""
"uuid:ada06e02-7394-4590-85da-57156f5b524d","http://resolver.tudelft.nl/uuid:ada06e02-7394-4590-85da-57156f5b524d","Multiscale simulation of inelastic creep deformation for geological rocks","Ramesh Kumar, K. (TU Delft Reservoir Engineering); Hajibeygi, H. (TU Delft Reservoir Engineering)","","2021","Subsurface geological formations provide giant capacities for large-scale (TWh) storage of renewable energy, once this energy (e.g. from solar and wind power plants) is converted to green gases, e.g. hydrogen. The critical aspects of developing this technology to full-scale will involve estimation of storage capacity, safety, and efficiency of a subsurface formation. Geological formations are often highly heterogeneous and, when utilized for cyclic energy storage, entail complex nonlinear rock deformation physics. In this work, we present a novel computational framework to study rock deformation under cyclic loading, in presence of nonlinear time-dependent creep physics. Both classical and relaxation creep methodologies are employed to analyze the variation of the total strain in the specimen over time. Implicit time-integration scheme is employed to preserve numerical stability, due to the nonlinear process. Once the computational framework is consistently defined using finite element method on the fine scale, a multiscale strategy is developed to represent the nonlinear deformation not only at fine but also coarser scales. This is achieved by developing locally computed finite element basis functions at coarse scale. The developed multiscale method also allows for iterative error reduction to any desired level, after being paired with a fine-scale smoother. Numerical test cases are studied to investigate various aspects of the developed computational workflow, from benchmarking with experiments to analysing the impact of nonlinear deformation for a field-scale relevant environment. Results indicate the applicability of the developed multiscale method in order to employ nonlinear physics in their laboratory-based scale of relevance (i.e., fine scale), yet perform field-relevant simulations. The developed simulator is made publicly available at https://gitlab.tudelft.nl/ADMIRE_Public/mechanics.","Algebraic multiscale method; Geomechanics; Multiscale basis functions; Nonlinear material deformation; Scalable physics-based nonlinear simulation; Subsurface energy storage","en","journal article","","","","","","","","","","","Reservoir Engineering","","",""
"uuid:9402aaf0-9c4f-4063-912d-891dc5f7c13a","http://resolver.tudelft.nl/uuid:9402aaf0-9c4f-4063-912d-891dc5f7c13a","Nitsche's method as a variational multiscale formulation and a resulting boundary layer fine-scale model","Stoter, Stein K.F. (Leibniz University Hannover); ten Eikelder, M.F.P. (TU Delft Ship Hydromechanics and Structures); de Prenter, Frits (Eindhoven University of Technology); Akkerman, I. (TU Delft Ship Hydromechanics and Structures); van Brummelen, E. Harald (Eindhoven University of Technology); Verhoosel, Clemens V. (Eindhoven University of Technology); Schillinger, Dominik (Leibniz University Hannover)","","2021","We show that in the variational multiscale framework, the weak enforcement of essential boundary conditions via Nitsche's method corresponds directly to a particular choice of projection operator. The consistency, symmetry and penalty terms of Nitsche's method all originate from the fine-scale closure dictated by the corresponding scale decomposition. As a result of this formalism, we are able to determine the exact fine-scale contributions in Nitsche-type formulations. In the context of the advection–diffusion equation, we develop a residual-based model that incorporates the non-vanishing fine scales at the Dirichlet boundaries. This results in an additional boundary term with a new model parameter. We then propose a parameter estimation strategy for all parameters involved that is also consistent for higher-order basis functions. We illustrate with numerical experiments that our new augmented model mitigates the overly diffusive behavior that the classical residual-based fine-scale model exhibits in boundary layers at boundaries with weakly enforced essential conditions.","Boundary layer accuracy; Fine-scale Green's function; Higher-order basis functions; Nitsche's method; Variational multiscale method; Weak boundary conditions","en","journal article","","","","","","Accepted Author Manuscript","","2022-05-05","","","Ship Hydromechanics and Structures","","",""
"uuid:be5439f7-09a3-4ca3-8b44-e1bc634a200d","http://resolver.tudelft.nl/uuid:be5439f7-09a3-4ca3-8b44-e1bc634a200d","A theoretical framework for discontinuity capturing: Joining variational multiscale analysis and variation entropy theory","ten Eikelder, M.F.P. (TU Delft Ship Hydromechanics and Structures); Bazilevs, Y. (Brown University); Akkerman, I. (TU Delft Ship Hydromechanics and Structures)","","2020","In this paper we show that the variational multiscale method together with the variation entropy concept form the underlying theoretical framework of discontinuity capturing. The variation entropy [M.F.P. ten Eikelder and I. Akkerman, Comput. Methods Appl. Mech. Engrg. 355 (2019) 261-283] is the recently introduced concept that equips total variation diminishing solutions with an entropy foundation. This is the missing ingredient in order to show that the variational multiscale method can capture sharp layers. The novel framework naturally equips the variational multiscale method with a class of discontinuity capturing operators. This class includes the popular YZβ method and methods based on the residual of the variation-entropy. The discontinuity capturing mechanisms do not contain ad hoc devices and appropriate length scales are derived. Numerical results obtained with quadratic NURBS are virtually oscillation-free and show sharp layers, which confirms the viability of the methodology.","Discontinuity capturing operators; Isogeometric analysis; TVD property; Variation entropy; Variation entropy residual-based; Variational multiscale method","en","journal article","","","","","","Accepted Author Manuscript","","2022-01-02","","","Ship Hydromechanics and Structures","","",""
"uuid:cadf667d-4928-4c8c-b0f9-40ffed1b0f49","http://resolver.tudelft.nl/uuid:cadf667d-4928-4c8c-b0f9-40ffed1b0f49","Iterative multiscale gradient computation for heterogeneous subsurface flow","Jesus de Moraes, R. (TU Delft Reservoir Engineering; Petrobras Research & Development Center); de Zeeuw, W. (TU Delft Electrical Engineering, Mathematics and Computer Science); R. P. Rodrigues, José (Petrobras Research & Development Center); Hajibeygi, H. (TU Delft Reservoir Engineering); Jansen, J.D. (TU Delft Civil Engineering & Geosciences; TU Delft Geoscience and Engineering)","","2019","We introduce a semi-analytical iterative multiscale derivative computation methodology that allows for error control and reduction to any desired accuracy, up to fine-scale precision. The model responses are computed by the multiscale forward simulation of flow in heterogeneous porous media. The derivative computation method is based on the augmentation of the model equation and state vectors with the smoothing stage defined by the iterative multiscale method. In the formulation, we avoid additional complexity involved in computing partial derivatives associated to the smoothing step. We account for it as an approximate derivative computation stage. The numerical experiments illustrate how the newly introduced derivative method computes misfit objective function gradients that converge to fine-scale one as the iterative multiscale residual converges. The robustness of the methodology is investigated for test cases with high contrast permeability fields. The iterative multiscale gradient method casts a promising approach, with minimal accuracy-efficiency tradeoff, for large-scale heterogeneous porous media optimization problems.","Adjoint method; Direct method; Gradient computation; Iterative multiscale finite volume; Multiscale methods; Subsurface flow","en","journal article","","","","","","","","","Electrical Engineering, Mathematics and Computer Science","Geoscience and Engineering","Reservoir Engineering","","",""
"uuid:604d8ddd-8620-4665-9aca-db4e9c8451c4","http://resolver.tudelft.nl/uuid:604d8ddd-8620-4665-9aca-db4e9c8451c4","An Efficient Robust Optimization Workflow using Multiscale Simulation and Stochastic Gradients","Jesus de Moraes, R. (TU Delft Reservoir Engineering; Petrobras); Fonseca, Rahul-Mark (TNO); Helici, Mircea A. (TNO); Heemink, A.W. (TU Delft Mathematical Physics); Jansen, J.D. (TU Delft Geoscience and Engineering)","","2019","We present an efficient workflow that combines multiscale (MS) forward simulation and stochastic gradient computation - MS-StoSAG - for the optimization of well controls applied to waterflooding under geological uncertainty. A two-stage iterative Multiscale Finite Volume (i-MSFV), a mass conservative reservoir simulation strategy, is employed as the forward simulation strategy. MS methods provide the ability to accurately capture fine scale heterogeneities, and thus the fine-scale physics of the problem, while solving for the primary variables in a more computationally efficient coarse-scale simulation grid. In the workflow, the construction of the basis fuctions is performed at an offline stage and they are not reconstructed/updated throughout the optimization process. Instead, inaccuracies due to outdated basis functions are addressed by the i-MSFV smoothing stage. The Stochastic Simplex Approximate Gradient (StoSAG) method, a stochastic gradient technique is employed to compute the gradient of the objective function using forward simulation responses. Our experiments illustrate that i-MSFV simulations provide accurate forward simulation responses for the gradient computation, with the advantage of speeding up the workflow due to faster simulations. Speed-ups up to a factor of five on the forward simulation, the most computationally expensive step of the optimization workflow, were achieved for the examples considered in the paper. Additionally, we investigate the impact of MS parameters such as coarsening ratio and heterogeneity contrast on the optimization process. The combination of speed and accuracy of MS forward simulation with the flexibility of the StoSAG technique allows for a flexible and efficient optimization workflow suitable for large-scale problems.","Gradient-based optimization; multiscale methods; Robust optimization; Stochastic gradient","en","journal article","","","","","","","","","","Geoscience and Engineering","Reservoir Engineering","","",""
"uuid:0ce45ddb-4932-4808-aa92-bd13deb85fa9","http://resolver.tudelft.nl/uuid:0ce45ddb-4932-4808-aa92-bd13deb85fa9","Algebraic Multiscale Framework for Fractured Reservoir Simulation","Tene, M. (TU Delft Reservoir Engineering)","Jansen, J.D. (promotor); Hajibeygi, H. (copromotor); Delft University of Technology (degree granting institution)","2018","Despite welcome increases in the adoption of renewable energy sources, oil and natural gas are likely to remain the main ingredient in the global energy diet for the decades to come. Therefore, the efficient exploitation of existing suburface reserves is essential for the well-being of society. This has stimulated recent developments in computer models able to provide critical insight into the evolution of the flow of water, gas and hydrocarbons through rock pores. Any such endeavour, however, has to tackle a number of challenges, including the considerable size of the domain, the highly heterogeneous spatial distribution of geological properties, as well as the intrinsic uncertainty and limitations associated with field data acquisition. In addition, the naturally-formed or artificially induced networks of fractures, present in the rock, require special treatment, due to their complex geometry and crucial impact on fluid flow patterns.
From a numerical point of view, a reservoir simulator’s operation entails the solution of a series linear systems, as dictated by the spatial and temporal discretization of the governing equations. The difficulty lies in the properties of these systems, which are large, ill-conditioned and often have an irregular sparsity pattern. Therefore, a brute-force approach, where the solutions are directly computed at the original fine-scale resolution, is often an impractically expensive venture, despite recent advances in parallel computing hardware. On the other hand, switching to a coarser resolution to obtain faster results, runs the risk of omitting important features of the flow, which is especially true in the case of fractured porous media.
This thesis describes an algebraic multiscale approach for fractured reservoir simulation. Its purpose is to offer a middle-ground, by delivering results at the
original resolution, while solving the equations on the coarse-scale. This is made possible by the so-called basis functions – a set of locally-supported cross-scale interpolators, conforming to the heterogeneities in the domain. The novelty of the work lies in the extension of these methods to capture the effect of fractures. Importantly, this is done in fully algebraic fashion, i.e. without making any assumptions regarding geometry or conductivity properties.
In order to elicit the generality of the proposed approach, a series of sensitivity studies are conducted on a proof-of-concept implementation. The results, which include both CPU times and convergence behaviour, are discussed and compared to those obtained using an industrial-grade AMG package. They serve as benchmarks, recommending the inclusion of multiscale methods in next-generation commercial reservoir simulators.","algebraic multiscale methods; naturally fractured porous media; conductivity contrasts; compressible flow; multiphase transport","en","doctoral thesis","","978-94-6186-956-2","","","","","","","","","Reservoir Engineering","","",""
"uuid:d4706f01-2f6d-45c5-8f6d-9d35a1f1a22b","http://resolver.tudelft.nl/uuid:d4706f01-2f6d-45c5-8f6d-9d35a1f1a22b","A discontinuous Galerkin residual-based variational multiscale method for modeling subgrid-scale behavior of the viscous Burgers equation","Stoter, Stein K.F. (University of Minnesota Twin Cities); Turteltaub, S.R. (TU Delft Aerospace Structures & Computational Mechanics); Hulshoff, S.J. (TU Delft Aerodynamics); Schillinger, Dominik (University of Minnesota Twin Cities)","","2018","We initiate the study of the discontinuous Galerkin residual-based variational multiscale (DG-RVMS) method for incorporating subgrid-scale behavior into the finite element solution of hyperbolic problems. We use the one-dimensional viscous Burgers equation as a model problem, as its energy dissipation mechanism is analogous to that of turbulent flows. We first develop the DG-RVMS formulation for a general class of nonlinear hyperbolic problems with a diffusion term, based on the decomposition of the true solution into discontinuous coarse-scale and fine-scale components. In contrast to existing continuous variational multiscale methods, the DG-RVMS formulation leads to additional fine-scale element interface terms. For the Burgers equation, we devise suitable models for all fine-scale terms that do not use ad hoc devices such as eddy viscosities but instead directly follow from the nature of the fine-scale solution. In comparison to single-scale discontinuous Galerkin methods, the resulting DG-RVMS formulation significantly reduces the energy error of the Burgers solution, demonstrating its ability to incorporate subgrid-scale behavior in the discrete coarse-scale system.","Burgers turbulence; Discontinuous Galerkin methods; Residual-based multiscale modeling; Variational multiscale method","en","journal article","","","","","","Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.","","2019-02-01","","","Aerospace Structures & Computational Mechanics","","",""
"uuid:e3f5a9df-2c73-40fd-a51b-d4ba6469c9e6","http://resolver.tudelft.nl/uuid:e3f5a9df-2c73-40fd-a51b-d4ba6469c9e6","Algebraic dynamic multilevel method for embedded discrete fracture model (F-ADM)","Hosseinimehr, S.M. (TU Delft Numerical Analysis); Cusini, M. (TU Delft Reservoir Engineering); Vuik, Cornelis (TU Delft Numerical Analysis); Hajibeygi, H. (TU Delft Reservoir Engineering)","","2018","We present an algebraic dynamic multilevel method for multiphase flow in heterogeneous fractured porous media (F-ADM), where fractures are resolved at fine scale with an embedded discrete modelling approach. This fine-scale discrete system employs independent fine-scale computational grids for heterogeneous matrix and discrete fractures, which results in linear system sizes out of the scope of the classical simulation approaches. To reduce the computational costs, yet provide accurate solutions, on this highly resolved fine-scale mesh, F-ADM imposes independent dynamic multilevel coarse grids for both matrix and lower-dimensional discrete fractures. The fully-implicit discrete system is then mapped into this adaptive dynamic multilevel resolution for all unknowns (i.e., pressure and phase saturation). The dynamic resolution aims for resolving sharp fronts for the transport unknowns, thus constant interpolators are used to map the saturation from coarse to fine grids both in matrix and fractures. However, due to the global nature of the pressure unknowns, local multilevel basis functions for both matrix and fractures with flexible matrix-fracture coupling treatment are introduced for the pressure. The assembly of the full sets of basis functions allows for mapping the solutions up and down between any resolutions. Due to its adaptive multilevel resolution, F-ADM develops an automatic integrated framework to homogenise or explicitly represent a fracture network at a coarser level by selection of the multilevel coarse nodes in each sub-domain. Various test cases, including multiphase flow in 2D and 3D media, are studied, where only a fraction of the fine-scale grids is employed to obtain accurate nonlinear multiphase solutions. F-ADM casts a promising approach for large-scale simulation of multiphase flow in fractured media.","Adaptive mesh refinement; Algebraic multiscale method; Flow in porous media; Fractured porous media; Multilevel multiscale method; Multiscale basis functions; Scalable physics-based nonlinear simulation","en","journal article","","","","","","Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.","","","","","Numerical Analysis","","",""
"uuid:51505ede-0121-4b24-aebe-07d45193e3fc","http://resolver.tudelft.nl/uuid:51505ede-0121-4b24-aebe-07d45193e3fc","Correct energy evolution of stabilized formulations: The relation between VMS, SUPG and GLS via dynamic orthogonal small-scales and isogeometric analysis. I: The convective–diffusive context","ten Eikelder, M.F.P. (TU Delft Ship Hydromechanics and Structures); Akkerman, I. (TU Delft Ship Hydromechanics and Structures)","","2018","This paper presents the construction of novel stabilized finite element methods in the convective–diffusive context that exhibit correct-energy behavior. Classical stabilized formulations can create unwanted artificial energy. Our contribution corrects this undesired property by employing the concepts of dynamic as well as orthogonal small-scales within the variational multiscale framework (VMS). The desire for correct energy indicates that the large- and small-scales should be H0 1-orthogonal. Using this orthogonality the VMS method can be converted into the streamline-upwind Petrov–Galerkin (SUPG) or the Galerkin/least-squares (GLS) method. Incorporating both large- and small-scales in the energy definition asks for dynamic behavior of the small-scales. Therefore, the large- and small-scales are treated as separate equations. Two consistent variational formulations which depict correct-energy behavior are proposed: (i) the Galerkin/least-squares method with dynamic small-scales (GLSD) and (ii) the dynamic orthogonal formulation (DO). The methods are presented in combination with an energy-decaying generalized-α time-integrator. Numerical verification shows that dissipation due to the small-scales in classical stabilized methods can become negative, on both a local and a global scale. The results show that without loss of accuracy the correct-energy behavior can be recovered by the proposed methods. The computations employ NURBS-based isogeometric analysis for the spatial discretization.","Correct-energy behavior; Dynamic orthogonal small-scales; Isogeometric analysis; Residual-based variational multiscale method; Stabilized finite element methods","en","journal article","","","","","","Accepted Author Manuscript","","2019-12-11","","","Ship Hydromechanics and Structures","","",""
"uuid:d031111a-5862-49ac-98ac-c9553574fc2f","http://resolver.tudelft.nl/uuid:d031111a-5862-49ac-98ac-c9553574fc2f","Correct energy evolution of stabilized formulations: The relation between VMS, SUPG and GLS via dynamic orthogonal small-scales and isogeometric analysis. II: The incompressible Navier–Stokes equations","ten Eikelder, M.F.P. (TU Delft Ship Hydromechanics and Structures); Akkerman, I. (TU Delft Ship Hydromechanics and Structures)","","2018","This paper presents the construction of a correct-energy stabilized finite element method for the incompressible Navier–Stokes equations. The framework of the methodology and the correct-energy concept have been developed in the convective–diffusive context in the preceding paper [M.F.P. ten Eikelder, I. Akkerman, Correct energy evolution of stabilized formulations: The relation between VMS, SUPG and GLS via dynamic orthogonal small-scales and isogeometric analysis. I: The convective–diffusive context, Comput. Methods Appl. Mech. Engrg. 331 (2018) 259–280]. The current work extends ideas of the preceding paper to build a stabilized method within the variational multiscale (VMS) setting which displays correct-energy behavior. Similar to the convection–diffusion case, a key ingredient is the proper dynamic and orthogonal behavior of the small-scales. This is demanded for correct energy behavior and links the VMS framework to the streamline-upwind Petrov–Galerkin (SUPG) and the Galerkin/least-squares method (GLS). The presented method is a Galerkin/least-squares formulation with dynamic divergence-free small-scales (GLSDD). It is locally mass-conservative for both the large- and small-scales separately. In addition, it locally conserves linear and angular momentum. The computations require and employ NURBS-based isogeometric analysis for the spatial discretization. The resulting formulation numerically shows improved energy behavior for turbulent flows comparing with the original VMS method.","Energy decay; Incompressible flow; Isogeometric analysis; Orthogonal small-scales; Residual-based variational multiscale method; Stabilized methods","en","journal article","","","","","","Accepted Author Manuscript","","2020-03-07","","","Ship Hydromechanics and Structures","","",""
"uuid:b4fccf77-cd61-4434-9959-67670a39df38","http://resolver.tudelft.nl/uuid:b4fccf77-cd61-4434-9959-67670a39df38","Residual-based variational multiscale modeling in a discontinuous Galerkin framework","Stoter, Stein K.F. (University of Minnesota Twin Cities); Turteltaub, S.R. (TU Delft Aerospace Structures & Computational Mechanics); Hulshoff, S.J. (TU Delft Aerodynamics); Schillinger, Dominik (University of Minnesota Twin Cities)","","2018","We develop the general form of the variational multiscale method in a discontinuous Galerkin framework. Our method is based on the decomposition of the true solution into discontinuous coarse-scale and discontinuous fine-scale parts. The obtained coarse-scale weak formulation includes two types of fine-scale contributions. The first type corresponds to a fine-scale volumetric term, which we formulate in terms of a residual-based model that also takes into account fine-scale effects at element interfaces. The second type consists of independent fine-scale terms at element interfaces, which we formulate in terms of a new fine-scale ""interface model."" We demonstrate for the one-dimensional Poisson problem that existing discontinuous Galerkin formulations, such as the interior penalty method, can be rederived by choosing particular fine-scale interface models. The multiscale formulation thus opens the door for a new perspective on discontinuous Galerkin methods and their numerical properties. This is demonstrated for the one-dimensional advection-diffusion problem, where we show that upwind numerical fluxes can be interpreted as an ad hoc remedy for missing volumetric fine-scale terms.","Multiscale discontinuous Galerkin methods; Residual-based multiscale modeling; Upwinding; Variational multiscale method","en","journal article","","","","","","Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.","","2019-04-01","","","Aerospace Structures & Computational Mechanics","","",""
"uuid:ace246d6-efa7-47e8-9942-14d4d75ef04c","http://resolver.tudelft.nl/uuid:ace246d6-efa7-47e8-9942-14d4d75ef04c","Multiscale gradient computation for flow in heterogeneous porous media","Jesus de Moraes, R. (TU Delft Reservoir Engineering); Rodrigues, José R P (Petrobras); Hajibeygi, H. (TU Delft Reservoir Engineering); Jansen, J.D. (TU Delft Civil Engineering & Geosciences; TU Delft Geoscience and Engineering)","","2017","An efficient multiscale (MS) gradient computation method for subsurface flow management and optimization is introduced. The general, algebraic framework allows for the calculation of gradients using both the Direct and Adjoint derivative methods. The framework also allows for the utilization of any MS formulation that can be algebraically expressed in terms of a restriction and a prolongation operator. This is achieved via an implicit differentiation formulation. The approach favors algorithms for multiplying the sensitivity matrix and its transpose with arbitrary vectors. This provides a flexible way of computing gradients in a form suitable for any given gradient-based optimization algorithm. No assumption w.r.t. the nature of the problem or specific optimization parameters is made. Therefore, the framework can be applied to any gradient-based study. In the implementation, extra partial derivative information required by the gradient computation is computed via automatic differentiation. A detailed utilization of the framework using the MS Finite Volume (MSFV) simulation technique is presented. Numerical experiments are performed to demonstrate the accuracy of the method compared to a fine-scale simulator. In addition, an asymptotic analysis is presented to provide an estimate of its computational complexity. The investigations show that the presented method casts an accurate and efficient MS gradient computation strategy that can be successfully utilized in next-generation reservoir management studies.","Adjoint method; Automatic differentiation; Direct method; Gradient-based optimization; Multiscale methods","en","journal article","","","","","","Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.","","2017-08-14","Civil Engineering & Geosciences","Geoscience and Engineering","Reservoir Engineering","","",""
"uuid:c55b3ac8-ef38-4a34-ba54-2eaf44271b51","http://resolver.tudelft.nl/uuid:c55b3ac8-ef38-4a34-ba54-2eaf44271b51","Algebraic multiscale method for flow in heterogeneous porous media with embedded discrete fractures (F-AMS)","Tene, M. (TU Delft Reservoir Engineering); al Kobaisi, MS (Petroleum Institute); Hajibeygi, H. (TU Delft Reservoir Engineering)","","2016","This paper introduces an Algebraic MultiScale method for simulation of flow in heteroge-neous porous media with embedded discrete Fractures (F-AMS). First, multiscale coarse grids are independently constructed for both porous matrix and fracture networks. Then, amap between coarse-and fine-scale is obtained by algebraically computing basis functions with local support. In order to extend the localization assumption to the fractured media, four types of basis functions are investigated: (1)Decoupled-AMS, in which the two media are completely decoupled, (2)Frac-AMS and (3)Rock-AMS, which take into account only one-way transmissibilities, and (4)Coupled-AMS, in which the matrix and fracture interpolators are fully coupled. In order to ensure scalability, the F-AMS framework permits full flexibility in terms of the resolution of the fracture coarse grids. Numerical results are presented for two-and three-dimensional heterogeneous test cases. During these experiments, the performance of F-AMS, paired with ILU(0) as second-stage smoother in a convergent iterative procedure, is studied by monitoring CPU times and convergence rates. Finally, in order to investigate the scalability of the method, an extensive benchmark study is conducted, where a commercial algebraic multigrid solver is used as reference. The results show that, given an appropriate coarsening strategy, F-AMS is insensitive to severe fracture and matrix conductivity contrasts, as well as the length of the fracture networks. Its unique feature is that a fine-scale mass conservative flux field can be reconstructed after any iteration, providing efficient approximate solutions in time-dependent simulations.","Algebraic multiscale methods; Flow in porous media; Naturally fractured porous rock; Heterogeneous permeability; Scalable linear solvers","en","journal article","","","","","","","","2018-07-01","","","Reservoir Engineering","","",""
"uuid:34abdb6c-4610-4072-a35a-7cc7e4295383","http://resolver.tudelft.nl/uuid:34abdb6c-4610-4072-a35a-7cc7e4295383","Multiscale finite-element method for linear elastic geomechanics","Castelletto, N (Stanford University); Hajibeygi, H. (TU Delft Reservoir Engineering); Tchelepi, HA (Stanford University)","","2016","The demand for accurate and efficient simulation of geomechanical effects is widely increasing in the geoscience community. High resolution characterizations of the mechanical properties of subsurface formations are essential for improving modeling predictions. Such detailed descriptions impose severe computational challenges and motivate the development of multiscale solution strategies. We propose a multiscale solution framework for the geomechanical equilibrium problem of heterogeneous porous media based on the finite-element method. After imposing a coarsescale grid on the given fine-scale problem, the coarse-scale basis functions are obtained by solving local equilibrium problems within coarse elements. These basis functions form the restriction and prolongation operators used to obtain the coarse-scale system for the displacement-vector. Then, a two-stage preconditioner that couples the multiscale system with a smoother is derived for the iterative solution of the fine-scale linear system. Various numerical experiments are presented to demonstrate accuracy and robustness of the method.","Multiscale methods; multiscale finite-element method; geomechanics; reconditioning; porous media","en","journal article","","","","","","","","2018-12-01","","","Reservoir Engineering","","",""
"uuid:d7766216-cc42-46d0-87e8-878755ce2f59","http://resolver.tudelft.nl/uuid:d7766216-cc42-46d0-87e8-878755ce2f59","Multiscale thermomechanical analysis of multiphase materials","Yadegari Varnamkhasti, S.","Benedictus, R. (promotor); Suiker, A.S.J. (promotor); Turteltaub, S. (promotor)","2015","The thermomechanical simulation of materials with evolving, multiphase microstructures poses various modeling and numerical challenges. For example, the separate phases in a multiphase microstructure can interact with each other during thermal and/or mechanical loading, the effect of which is significantly more complicated than the individual behavior of the phases. The interactive behavior also depends on the specific volume fractions and spatial distribution of the individual phases. An accurate modeling of the phases requires a thermodynamically consistent formulation and a robust numerical implementation of the evolution of the corresponding observable and internal variables. The complex nonlinear characteristics of these micromechanical models introduce substantial challenges with respect to their upscaling towards higher levels of observation, as necessary for analyzing large-scale engineering problems in a computationally efficient way. The work presented in this thesis addresses these aspects in detail by focusing on a class of multiphase steels, which are the so-called transformation-induced plasticity (TRIP) steels. This class of structural steels shows an excellent combination of strength and ductility. The transformation-induced plasticity effect can be ascribed to the presence of grains of metastable austenite that are surrounded by ferritic grains. The austenite can undergo a phase transformation when subjected to thermal and/or mechanical loading, thereby introducing an increase in the effective material strength. In addition, both the austenite and the ferritic matrix may deform plastically, which increases the overall ductility of the material. In order to explore the complex micromechanical characteristics and the practical application of this material in more detail, three main research questions were identified, of which the first one is: (1) How can a TRIP steel microstructure be modelled in a fully thermodynamically consistent way? The thermomechanical coupling is particularly relevant since in TRIP steels the phase transformation occurring during mechanical loading is accompanied by the release of a substantial amount of energy (latent heat) that, in turn, affects the mechanical response of the material. The second research question formulated is: (2) How does the response of a TRIP steel microstructure depend on the spatial distribution of the austenitic phase within the ferritic matrix? From the viewpoint of practical applications, the attention here is focused on comparing the response of a TRIP steel sample with a banded austenitic microstructure to that of a sample with randomly distributed austenitic grains. Considering the large number of degrees of freedom of these and other engineering problems, a computationally efficient implementation of the micromechanical model is necessary. This issue is reflected by the third research question, which reads: (3) Is it possible to include the micromechanical constitutive behavior and geometry of the individual phases within an computationally efficient multiscale formulation? For answering the three research questions above, the thermomechanical behavior of the TRIP steel phases is modelled in a fully coupled way, where the generation of heat associated to the martensitic phase transformation and the plastic deformation are accounted for explicitly in the thermodynamic formulation. In analogy with the decomposition of the deformation, the entropy density is separated in a reversible contribution, a transformation contribution, a plasticity contribution and a thermal-mechanical coupling contribution. The last term follows from combining mechanical and thermal constitutive information of the individual phases with basic thermodynamical requirements. One of the observations resulting from this approach is that for a single crystal of austenite the increase in temperature associated with the latent heat of transformation reduces the transformation rate and significantly reduces the transformation-induced plasticity effect. However, for an aggregate of austenitic and ferritic grains, which is representative of a TRIP steel, the delay in the transformation-induced plasticity effect due to latent heat is relatively small, since the ferric matrix absorbs the latent heat generated in the austenite and thus effectively acts as a thermal sink. To evaluate the influence of the spatial distribution of the austenitic (secondary) phase within the ferritic matrix, the effective responses for banded and dispersed austenitic microstructures are computed by means of numerical homogenization. A comparison of these microstructures shows that banded microstructures may allow for plastic localization in the ferritic matrix, which, in comparison to dispersed microstructures, diminishes the strengthening effect provided by the austenitic phase. For the performance of more demanding computational simulations at higher (macroscopic) scales of observation, an efficient multiscale approach termed the generalized grain cluster method (GGCM) was developed. The method is suitable for the prediction of the effective macroscopic behavior of an aggregate of single-crystal grains composing a multiphase steel. The GGCM is based on the minimization of a functional that depends on the microscopic deformation gradients in the grains through the equilibrium requirements of the grains as well as kinematic compatibility between grains. By means of the specification of weighting factors it is possible to mimic responses falling between the Taylor and Sachs bounds. The numerical computation is carried out with an incremental-iterative algorithm based on a constrained gradient descent method. For a multiscale analysis, the GCCM can be included at integration points of a standard finite element code to simulate macroscopic problems. A comparison with FEM direct numerical simulations illustrates that the computational time of the GGCM may be up to about an order of magnitude lower. In large-scale FEM models for structural applications, the responses at material point level thus may either follow from the GGCM alone, or from combining this method with fully-resolved FEM modeling at the level of individual grains (i.e., a combined GGCM - FE2 approach), depending on the required resolution.","multiscale methods; thermomechanical modeling; multiphase materials","en","doctoral thesis","","","","","","","","","Aerospace Engineering","Aerospace Structures and Materials (ASM)","","","",""
"uuid:16511dd6-dbb6-4c1e-b502-f770d860aa09","http://resolver.tudelft.nl/uuid:16511dd6-dbb6-4c1e-b502-f770d860aa09","Monotone multiscale finite volume method","Wang, Y.; Hajibeygi, H.; Tchelepi, H.A.","","2015","The MultiScale Finite Volume (MSFV) method is known to produce non-monotone solutions. The causes of the non-monotone solutions are identified and connected to the local flux across the boundaries of primal coarse cells induced by the basis functions. We propose a monotone MSFV (m-MSFV) method based on a local stencil-fix that guarantees monotonicity of the coarse-scale operator, and thus, the resulting approximate fine-scale solution. Detection of non-physical transmissibility coefficients that lead to non-monotone solutions is achieved using local information only and is performed algebraically. For these ‘critical’ primal coarse-grid interfaces, a monotone local flux approximation, specifically, a Two-Point Flux Approximation (TPFA), is employed. Alternatively, a local linear boundary condition can be used for the dual basis functions to reduce the degree of non-monotonicity. The local nature of the two strategies allows for ensuring monotonicity in local sub-regions, where the non-physical transmissibility occurs. For practical applications, an adaptive approach based on normalized positive off-diagonal coarse-scale transmissibility coefficients is developed. Based on the histogram of these normalized coefficients, one can remove the large peaks by applying the proposed modifications only for a small fraction of the primal coarse grids. Though the m-MSFV approach can guarantee monotonicity of the solutions to any desired level, numerical results illustrate that employing the m-MSFV modifications only for a small fraction of the domain can significantly reduce the non-monotonicity of the conservative MSFV solutions.","multiscale finite volume method; iterative multiscale methods; algebraic multiscale solver; scalable linear solvers; monotone flux approximation schemes; multipoint flux approximation; porous media","en","journal article","Springer","","","","","","","","Civil Engineering and Geosciences","Geoscience & Engineering","","","",""
"uuid:3d828e1d-59e3-44cc-8cd0-b29649ef8e6c","http://resolver.tudelft.nl/uuid:3d828e1d-59e3-44cc-8cd0-b29649ef8e6c","Generalized grain cluster method for multiscale response of multiphase materials","Yadegari, S.; Turteltaub, S.R.; Suiker, A.S.J.","","2015","A multiscale approach termed the generalized grain cluster method (GGCM) is presented, which can be applied for the prediction of the macroscopic behavior of an aggregate of single crystal grains composing a multiphase material. The GGCM is based on the minimization of a functional that depends on the microscopic deformation gradients in the grains through the equilibrium requirements of the grains as well as kinematic compatibility between grains. By means of the specification of weighting factors it is possible to mimic responses falling between the Taylor and Sachs bounds. The numerical solution is computed with an incremental-iterative algorithm based on a constrained gradient descent method. For a multiscale analysis, the GCCM can be included at integration points of a standard finite element code to simulate macroscopic problems. A comparison with FEM direct numerical simulations illustrates that the computational time of the GGCM may be up to about an order of magnitude lower.","multiscale method; homogenization; grain cluster; multiphase material; TRIP steel","en","journal article","Springer","","","","","","","","Aerospace Engineering","Aerospace Structures & Materials","","","",""
"uuid:ee7cda21-080c-4194-82f7-588de9cd32f4","http://resolver.tudelft.nl/uuid:ee7cda21-080c-4194-82f7-588de9cd32f4","Generalized grain cluster method for multiscale response of multiphase materials","Yadegari Varnamkhasti, S. (TU Delft Aerospace Structures & Computational Mechanics); Turteltaub, S.R. (TU Delft Aerospace Structures & Computational Mechanics); Suiker, A.S.J. (Eindhoven University of Technology)","","2015","A multiscale approach termed the generalized grain cluster method (GGCM) is presented, which can be applied for the prediction of the macroscopic behavior of an aggregate of single crystal grains composing a multiphase material. The GGCM is based on the minimization of a functional that depends on the microscopic deformation gradients in the grains through the equilibrium requirements of the grains as well as kinematic compatibility between grains. By means of the specification of weighting factors it is possible to mimic responses falling between the Taylor and Sachs bounds. The numerical solution is computed with an incremental-iterative algorithm based on a constrained gradient descent method. For a multiscale analysis, the GCCM can be included at integration points of a standard finite element code to simulate macroscopic problems. A comparison with FEM direct numerical simulations illustrates that the computational time of the GGCM may be up to about an order of magnitude lower.","Multiscale method; Homogenization; Grain cluster; Multiphase material; TRIP steel","en","journal article","","","","","","","","","","","Aerospace Structures & Computational Mechanics","","",""
"uuid:03091774-0ba4-418a-bd12-9862dd7c4458","http://resolver.tudelft.nl/uuid:03091774-0ba4-418a-bd12-9862dd7c4458","Stabilisation Parameter Determination for the Stokes Equations","Chen, L.; Maher, G.D.; Hulshoff, S.J.","","2014","Parameters for SGS models within the variational multiscale method for the Stokes equations are determined using two different methods. Both linear and nonlinear models are considered. Firstly, optimal parameters are found using a goal-oriented model-constrained technique minimising L2 error. Secondly, parameters are obtained using the variational Germano identity. Using the goal-oriented results as reference values, it is shown that the performance of the Germano approach is sensitive to the form of the SGS model.","Variational Multiscale Method; stoke equations; stabilisation parameters; goal-oriented optimisation; Variational Germano Identity","en","conference paper","CIMNE","","","","","","","","Aerospace Engineering","Aerodynamics, Wind Energy & Propulsion","","","",""
"uuid:9dff055c-eb6d-4005-a052-fce8aaeea792","http://resolver.tudelft.nl/uuid:9dff055c-eb6d-4005-a052-fce8aaeea792","Numerical Methods for the Optimization of Nonlinear Residual-Based Sungrid-Scale Models Using the Variational Germano Identity","Maher, G.D.; Hulshoff, S.J.","","2014","The Variational Germano Identity [1, 2] is used to optimize the coefficients of residual-based subgrid-scale models that arise from the application of a Variational Multiscale Method [3, 4]. It is demonstrated that numerical iterative methods can be used to solve the Germano relations to obtain values for the parameters of subgrid-scale models that are nonlinear in their coefficients. Specifically, the Newton-Raphson method is employed. A least-squares minimization formulation of the Germano Identity is developed to resolve issues that occur when the residual is positive and negative over different regions of the domain. In this case a Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm is used to solve the minimization problem. The developed method is applied to the one-dimensional unsteady forced Burgers’ equation and the two-dimensional steady Stokes’ equations. It is shown that the Newton-Raphson method and BFGS algorithm generally solve, or minimize the residual of, the Germano relations in a relatively small number of iterations. The optimized subgridscale models are shown to outperform standard SGS models with respect to a L2 error. Additionally, the nonlinear SGS models tend to achieve lower L2 errors than the linear models.","subgrid-scale model; variational multiscale method; variational Germano identity; optimization; turbulence","en","conference paper","CIMNE","","","","","","","","Aerospace Engineering","Aerodynamics, Wind Energy & Propulsion","","","",""
"uuid:fffb011c-5c89-4f14-bf80-5f4727670ae9","http://resolver.tudelft.nl/uuid:fffb011c-5c89-4f14-bf80-5f4727670ae9","A Hard Constraint Algorithm to Model Particle Interactions in DNA-laden Micro Flows","Trebotich, D.; Miller, G.H.; Bybee, M.D.","","2006","We present a new method for particle interactions in polymer models of DNA. The DNA is represented by a bead-rod polymer model. The main objective in this work is to implement short range forces to properly model polymer-polymer and polymer-surface interactions. We will discuss two methods for these interactions: (1) a new rigid constraint algorithm whereby rods elastically bounce off one another, and (2) a classical (smooth) potential acting between rods. In addition, a smooth potential for the polymer-surface interactions is also implemented for comparison to the same interactions currently modeled by elastic collision.","microfluidics; DNA flows; fluid-particle coupling; multiscale methods","en","conference paper","","","","","","","","","","","","","",""
"uuid:1c36aa14-af05-4107-8a99-e16936492a7b","http://resolver.tudelft.nl/uuid:1c36aa14-af05-4107-8a99-e16936492a7b","Stabilized FEM for incompressible flow: A critical review and new trends","Lube, G.","","2006","The numerical solution of the nonstationary, incompressible Navier-Stokes model can be split into linearized auxiliary problems of Oseen type. We present in a unique way different stabilization techniques of finite element schemes on isotropic and hybrid meshes. First we describe the state-of-the-art for the classical residual-based SUPG/PSPG method. Then we discuss recent symmetric stabilization techniques which avoid some drawbacks of the classical method. These methods are closely related to the concept of variational multiscale methods which provides a new approach to large eddy simulation.","incompressible flow; Navier-Stokes equations; stabilized finite elements; variational multiscale methods; subgrid viscosity","en","conference paper","","","","","","","","","","","","","",""
"uuid:2f79e842-a961-416c-a2b9-3e775fd1d37f","http://resolver.tudelft.nl/uuid:2f79e842-a961-416c-a2b9-3e775fd1d37f","On finite element variational multiscale methods for incompressible turbulent flows","John, V.; Tambulea, A.","","2006","Two realizations of finite element variational multiscale (VMS) methods for the simulation of incompressible turbulent flows are studied. The difference between the two approaches consists in the way the spaces for the large scales and the resolved small scales are chosen. The paper addresses issues of the implementation of these methods, the treatment of the additional terms and equations in the temporal discretization, and the additional costs of these methods.","NavierStokes equations; incompressible turbulent flow; variational multiscale method; finite element method","en","conference paper","","","","","","","","","","","","","",""
"uuid:e055f69a-4edc-4f86-83fd-962465e71ee3","http://resolver.tudelft.nl/uuid:e055f69a-4edc-4f86-83fd-962465e71ee3","Multiscale Methods in Computational Fluid and Solid Mechanics","De Borst, R.; Hulshoff, S.J.; Lenz, S.; Munts, E.A.; Van Brummelen, E.H.; Wall, W.A.","","2006","The basic idea of multiscale methods, namely the decomposition of a problem into a coarse scale and a fine scale, has in an intuitive manner been used in engineering for many decades, if not for centuries. Also in computational science, large-scale problems have been solved, and local data, for instance displacements, forces or velocities, have been used as boundary conditions for the resolution of more detail in a part of the problem. Recent years have witnessed the development of multiscale methods in computational science, which strive at coupling fine scales and coarse scales in a more systematic manner. Having made a rigorous decomposition of the problem into fine scales and coarse scales, various approaches exist, which essentially only differ in how to couple the fine scales to the coarse scale. The Variational Multiscale Method is a most promising member of this family, but for instance, multigrid methods can also be classified as multiscale methods. The same conjecture can be substantiated for hp-adaptive methods. In this lecture we will give a succinct taxonomy of various multiscale methods. Next, we will briefly review the Variational Multiscale Method and we will propose a space-time VMS formulation for the compressible Navier-Stokes equations. The spatial discretization corresponds to a high-order continuous Galerkin method, which due to its hierarchical nature provides a natural framework for `a priori' scale separation. The latter property is crucial. The method is formulated to support both continuous and discontinuous discretizations in time. Results will be presented from the application of the method to the computation of turbulent channel flow. Finally, multigrid methods will be applied to fluid-structure interaction problems. The basic iterative method for fluid-structure interaction problems employs defect correction. The latter provides a suitable smoother for a multigrid process, although in itself the associated subiteration process converges slowly. Indeed, the smoothed error can be represented accurately on a coarse mesh, which results in an effective coarse-grid correction. It is noted that an efficient solution strategy is made possible by virtue of the relative compactness of the displacement-to-pressure operator in the fluid-structure interaction problem. This relative compactness manifests the difference in length and time scales in the fluid and the structure and, in this sense, the multigrid method exploits the inherent multiscale character of fluid-structure-interaction problems.","multiscale methods; fluid flow; turbulence; fluid-structure interaction; multigrid methods","en","conference paper","","","","","","","","","","","","","",""
"uuid:c2fb8e60-8b4e-446f-8535-c41372a3a9da","http://resolver.tudelft.nl/uuid:c2fb8e60-8b4e-446f-8535-c41372a3a9da","Multiscale Methods in Computational Fluid and Solid Mechanics","De Borst, R.; Hulshoff, S.J.; Lenz, S.; Munts, E.A.; Van Brummelen, E.H.; Wall, W.A.","","2006","The basic idea of multiscale methods, namely the decomposition of a problem into a coarse scale and a fine scale, has in an intuitive manner been used in engineering for many decades, if not for centuries. Also in computational science, large-scale problems have been solved, and local data, for instance displacements, forces or velocities, have been used as boundary conditions for the resolution of more detail in a part of the problem. Recent years have witnessed the development of multiscale methods in computational science, which strive at coupling fine scales and coarse scales in a more systematic manner. Having made a rigorous decomposition of the problem into fine scales and coarse scales, various approaches exist, which essentially only differ in how to couple the fine scales to the coarse scale. The Variational Multiscale Method is a most promising member of this family, but for instance, multigrid methods can also be classified as multiscale methods. The same conjecture can be substantiated for hp-adaptive methods. In this lecture we will give a succinct taxonomy of various multiscale methods. Next, we will briefly review the Variational Multiscale Method and we will propose a space-time VMS formulation for the compressible Navier-Stokes equations. The spatial discretization corresponds to a high-order continuous Galerkin method, which due to its hierarchical nature provides a natural framework for `a priori' scale separation. The latter property is crucial. The method is formulated to support both continuous and discontinuous discretizations in time. Results will be presented from the application of the method to the computation of turbulent channel flow. Finally, multigrid methods will be applied to fluid-structure interaction problems. The basic iterative method for fluid-structure interaction problems employs defect correction. The latter provides a suitable smoother for a multigrid process, although in itself the associated subiteration process converges slowly. Indeed, the smoothed error can be represented accurately on a coarse mesh, which results in an effective coarse-grid correction. It is noted that an efficient solution strategy is made possible by virtue of the relative compactness of the displacement-to-pressure operator in the fluid-structure interaction problem. This relative compactness manifests the difference in length and time scales in the fluid and the structure and, in this sense, the multigrid method exploits the inherent multiscale character of fluid-structure-interaction problems.","multiscale methods; fluid flow; turbulence; fluid-structure interaction; multigrid methods","en","conference paper","Delft University of Technology; European Community on Computational Methods in Applied Sciences (ECCOMAS)","","","","","","","","Aerospace Engineering","","","","",""
"uuid:3d168259-c397-4640-826e-a16bf315656c","http://resolver.tudelft.nl/uuid:3d168259-c397-4640-826e-a16bf315656c","Space-time multiscale methods for Large Eddy Simulation","Munts, E.A.","De Borst, R. (promotor)","2006","The Variational Multiscale (VMS) method has appeared as a promising new approach to the Large Eddy Simulation (LES) of turbulent flows. The key advantage of the VMS approach is that it allows different subgrid-scale (SGS) modeling assumptions to be made at different ranges of the resolved scales. Typically, in the VMS method, SGS modeling is confined to the smallest resolved scales, leaving the dynamically important large scales free from the direct influence of the SGS model. Prior implementations of the VMS approach have been restricted to either incompressible formulations, simple geometries and/or small time steps. We propose a space-time VMS method for the compressible Navier-Stokes equations, which aims to overcome the difficulties associated with prior VMS implementations. In particular, we aim to develop a method that is applicable to complex flow geometries with a minimum number of degrees of freedom, and that can march at time steps which are chosen to resolve the physical phenomena of interest rather than to satisfy stability constraints. The spatial discretization of the proposed computational approach corresponds to a high-order continuous Galerkin method, which due to its hierarchical nature provides a natural framework for 'a priori' scale separation, which is crucial for the VMS method. As the method is formulated in a space-time framework, it supports continuous as well as discontinuous discretizations in time. Time-discontinuous discretizations offer great flexibility for adaptation, but may be computationally expensive. Time-continuous discretizations, on the other hand, potentially offer a good compromise between accuracy and computational cost. We consider three different time discretizations, viz. a first-order time-continuous Galerkin method (TCG) in time, a second-order time-continuous Petrov-Galerkin method (TCPG) and a third-order discontinuous Galerkin method (TDG). We consider the efficacy of the spatial VMS discretization for the computation of fully-developed turbulent channel flow. We show that the present method leads to reduced resolution requirements compared to traditional LES approaches applying similar SGS models directly to all the resolved scales. The crucial parameter for obtaining reliable low-order statistics is found to be the large/small partition of the resolved scales. In particular, it is shown that when using simple eddy-viscosity models, the finite element basis functions capable of representing the basic dynamics of the near-wall coherent structures should be released from the direct influence of the SGS model. As space-time methods are necessarily implicit, a challenge is to ensure that the computations are carried out at reasonable cost. Therefore, we have conducted a detailed performance analysis to investigate the factors that influence the accuracy and computational cost of the proposed methods. For this purpose we consider again the turbulent channel flow. First, we examine the different time discretizations. It is demonstrated that the TCG method is not a competitive time discretization for the time steps of interest. The TCPG and TDG method, on the other hand, produce accurate and very similar results for relatively large time steps. However, the TDG method is considerably more computationally expensive as it uses twice the number of degrees of freedom compared to the TCPG method. Therefore, except for reasons of adaptation, the TCPG method is preferred here. Next, we compare the accuracy and cost of different spatial $hp$-resolutions for a similar total number of degrees of freedom. It is shown that the spatially higher-order methods lead to increased accuracy compared to a standard linear Galerkin method which cannot exploit the advantages of the present VMS formulation. However, higher-order methods are inherently expensive, as the computational work required within a time step scales quadratically with the number of finite element basis functions, while it scales only linear with the number of elements. Higher-order methods also have significantly denser system matrices resulting in rapidly increasing memory requirements with the order of the scheme. As the computational cost associated with higher-order methods is still relatively high, additional research areas are suggested for the goal of improving the method's cost efficiency.","space-time; finite element method; variational multiscale method; large eddy simulation","en","doctoral thesis","","","","","","","","","Aerospace Engineering","","","","",""