Towards efficient adjoint-based mesh optimization for predictive Large Eddy Simulation

This thesis contributes to the effective and efficient application of unsteady adjoint methods to Adaptive Mesh Refinement (AMR) for Large Eddy Simulation (LES). Three aspects, i.e., subgrid-scale model error, storage cost of high-dimensional data, and stability of the adjoint problem for turbulent flows, were studied to make adjoint-based mesh...

Balancing truncation and round-off errors in FEM: One-dimensional analysis

In finite element methods, the accuracy of the solution cannot increase indefinitely since the round-off error related to limited computer precision increases when the number of degrees of freedom (DoFs) is large enough. Because a priori information of the highest attainable accuracy is of great interest, we construct an innovative method to...

Towards adjoint-based mesh refinement for Large Eddy Simulation using reduced-order primal solutions: Preliminary 1D Burgers study

Adaptive Mesh Refinement (AMR) is potentially an effective way to automatically generate computational meshes for high-fidelity simulations such as Large Eddy Simulation (LES). When combined with adjoint methods, which are able to localize error contributions, AMR can generate meshes that are optimal for computing a physical quantity of...

Uncertainty quantification in particle image velocimetry and advances in time-resolved image and data analysis

Particle Image Velocimetry (PIV) is a well-established technique for the measurement of the flow velocity in a two or three-dimensional domain. As in any other technique, PIV data is affected by measurement errors, defined as the difference between the measured velocity and its actual value, which is unknown. Aim of uncertainty quantification is...

Goal-Oriented Error Estimation and Adaptivity for Free-Boundary Problems: The Shape-Linearization Approach

We develop duality-based a posteriori error estimates for functional outputs of solutions of free-boundary problems via shape-linearization principles. To derive an appropriate dual (linearized adjoint) problem, we linearize the domain dependence of the very weak form and goal functional of interest using techniques from shape calculus. We show...

Goal-Oriented Error Estimation and Adaptivity for Free-Boundary Problems: The Domain-Map Linearization Approach

In free-boundary problems, the accuracy of a goal quantity of interest depends on both the accuracy of the approximate solution and the accuracy of the domain approximation. We develop duality-based a posteriori error estimates for functional outputs of solutions of free-boundary problems that include both sources of error. The derivation of an...

Goal-Oriented A-Posteriori Error Estimation and Adaptivity for Fluid-Structure Interaction

Numerical simulation of fluid-structure interaction generally requires vast computational resources. Paradoxically, the computational work is dominated by the complexity of the subsystem that is of least practical interest, viz. the fluid. The resolution of each of the many small-scale features in the fluid is prohibitively expensive. However,...

Adaptive Finite Element Approximation of Fluid-Structure Interaction Based on an Eulerian Variational Formulation

We propose a general variational framework for the adaptive finite element approximation of fluid-structure interaction problems. The modeling is based on an Eulerian description of the (incompressible) fluid as well as the (elastic) structure dynamics. This is achieved by tracking the movement of the initial positions of all `material' points....

Dual-based a-posteriori error estimation for fluid-structure interaction by the embedded-domain method

Numerical simulations of fluid-structure interaction typically require vast computational resources. Finite-element techniques employing goal-oriented hp-adaptation strategies could offer a substantial improvement in the efficiency of such simulations. These strategies rely on dual-based a-posteriori error estimates for quantities of interest....

Dual-based a-posteriori error estimation for fluid-structure interaction by the embedded-domain method

Numerical simulations of fluid-structure interaction typically require vast computational resources. Finite-element techniques employing goal-oriented hp-adaptation strategies could offer a substantial improvement in the efficiency of such simulations. These strategies rely on dual-based a-posteriori error estimates for quantities of interest....

A Reduced Basis Element Method for Complex Flow Systems

The reduced basis element method is a new approach for approximating the solution of problems described by partial differential equations within domains belonging to a certain class. The method takes its roots in domain decomposition methods and reduced basis discretizations. The basic idea is to first decompose the computational domain into...

Multiscale multi-dimensional explicit a-posteriori error estimation for fluid dynamics

A-posteriori error estimation of convection-dominated and hyperbolic flow problems remains one of the largest challenges in computational mechanics. The available techniques are either non-robust (i.e. the predicted error differs by orders of magnitude from the exact error) or computationally involved (i.e. requiring the solution of additional...