Searched for: subject%3A%22discontinuous%255C+galerkin%255C+methods%22
(1 - 20 of 26)

Pages

List view
Grid view
document
Kaaks, B.J. (author), Rohde, M. (author), Kloosterman, J.L. (author), Lathouwers, D. (author)
We present a discontinuous Galerkin method for melting/solidification problems based on the “linearized enthalpy approach,” which is derived from the conservative form of the energy transport equation and does not depend on the use of a so-called mushy zone. We use the symmetric interior penalty method and the Lax–Friedrichs flux to...
journal article 2023
document
Li, Xiaozhou (author), Ryan, J.K. (author), Kirby, Robert M. (author), Vuik, Cornelis (author)
Smoothness-increasing accuracy-conserving (SIAC) filtering is an area of increasing interest because it can extract the “hidden accuracy” in discontinuous Galerkin (DG) solutions. It has been shown that by applying a SIAC filter to a DG solution, the accuracy order of the DG solution improves from order k+ 1 to order 2 k+ 1 for linear...
journal article 2019
document
Geevers, S. (author), Mulder, W.A. (author), van der Vegt, J. J.W. (author)
We analyse the dispersion properties of two types of explicit finite element methods for modelling acoustic and elastic wave propagation on tetrahedral meshes, namely mass-lumped finite element methods and symmetric interior penalty discontinuous Galerkin methods, both combined with a suitable Lax–Wendroff time integration scheme. The...
journal article 2018
document
Stoter, Stein K.F. (author), Turteltaub, S.R. (author), Hulshoff, S.J. (author), Schillinger, Dominik (author)
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...
journal article 2018
document
Stoter, Stein K.F. (author), Turteltaub, S.R. (author), Hulshoff, S.J. (author), Schillinger, Dominik (author)
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...
journal article 2018
document
van Zwieten, J.S.B. (author), Sanderse, B. (author), Hendrix, M.H.W. (author), Vuik, Cornelis (author), Henkes, R.A.W.M. (author)
One-dimensional models for multiphase flow in pipelines are commonly discretised using first-order Finite Volume (FV) schemes, often combined with implicit time-integration methods. While robust, these methods introduce much numerical diffusion depending on the number of grid points. In this paper we propose a high-order, space-time...
journal article 2017
document
Vuik, M.J. (author)
This dissertation addresses practical use of multiwavelets and outlier detection for troubled-cell indication for discontinuous Galerkin (DG) methods. For smooth solutions, the DG approximation converges to the exact solution with a high order of accuracy. However, problems may arise when shock waves or discontinuities appear: non-physical...
doctoral thesis 2017
document
Vuik, M.J. (author), Ryan, J.K. (author)
In Vuik and Ryan [J. Comput. Phys., 270 (2014), pp. 138--160] we studied the use of troubled-cell indicators for discontinuity detection in nonlinear hyperbolic partial differential equations and introduced a new multiwavelet technique to detect troubled cells. We found that these methods perform well as long as a suitable, problem-dependent...
journal article 2016
document
Li, X. (author)
In this dissertation, we focus on exploiting superconvergence for discontinuous Galerkin methods and constructing a superconvergence extraction technique, in particular, Smoothness-Increasing Accuracy-Conserving (SIAC) filtering. The SIAC filtering technique is based on the superconvergence property of discontinuous Galerkin methods and aims to...
doctoral thesis 2015
document
Ye, B. (author)
This project focuses on extending the existing model for two-dimensional laminar boundary layers to turbulent boundary layers and more importantly to include the modeling of transition to turbulence in unsteady boundary layers. The existing models are extended and a new transition model for unsteady boundary layers is developed. Successful...
master thesis 2015
document
Ølgaard, K.B. (author)
In engineering, physical phenomena are often described mathematically by partial differential equations (PDEs), and a commonly used method to solve these equations is the finite element method (FEM). Implementing a solver based on this method for a given PDE in a computer program written in source code can be tedious, time consuming and error...
doctoral thesis 2013
document
Koeze, D.J. (author)
In this work we examined the discretised form of Boltzmann-like transport, i.e. the neutron trans- port equation and the Boltzmann-Fokker-Plank (BFP) equation with the discontinuous Galerkin method and polynomial basis functions. In particular we examined an adaptive algorithm, which bases its decision of where to refine on the adjoint problem,...
master thesis 2012
document
Ji, L. (author), Xu, Y. (author)
In (Xu and Shu in J. Sci. Comput. 40:375–390, 2009), a local discontinuous Galerkin (LDG) method for the surface diffusion of graphs was developed and a rigorous proof for its energy stability was given. Numerical simulation results showed the optimal order of accuracy. In this subsequent paper, we concentrate on analyzing a priori error...
journal article 2011
document
Özdemir, H. (author), Van den Boogaard, E.F. (author)
In this study the two-dimensional, unsteady integral boundary layer equations are solved numerically together with a closure set for laminar and turbulent flows. A high-order discontinuous Galerkin method is used for the spatial discretization and a multi-stage Runge-Kutta scheme is employed for the time integration. Numerical results show good...
conference paper 2011
document
Cheruvu, V. (author), Ryan, J.K. (author)
In this report, we present a multi-wavelet type limiter for the discontinuous Galerkin method for limiting the solution when spurious oscillations develop near a shock. This limiting leads to a loss of information in the approximation that can be detrimental to a higher order approximation (k > 2). The goal is therefore to retain as much...
report 2010
document
Ryan, J.K. (author)
Previous investigations into accuracy enhancement for the derivatives of a discontinuous Galerkin solution demonstrated that there are many ways to approach obtaining higher order accuracy in the derivatives, each with different advantageous properties [J.K. Ryan and B. Cockburn (2009), “Local Derivative Post-Processing for the Discontinuous...
report 2010
document
Cheruvu, V. (author), Ryan, J.K. (author)
In this report, we present a multi-wavelet type limiter for the discontinuous Galerkin method for limiting the solution when spurious oscillations develop near a shock. This limiting leads to a loss of information in the approximation that can be detrimental to a higher order approximation (k > 2). The goal is therefore to retain as much...
report 2010
document
Nguyen, T.D. (author)
A structural thin bending problem is essentially associated with a fourth-order partial differential equation. Within the finite element framework, the numerical solution of thin bending problems demands the use of C^1 continuous shape functions. Elements using these functions are challenging and difficult to construct. A particular...
doctoral thesis 2008
document
Lamine, S. (author), Edwards, M.G. (author)
Discontinuous-Galerkin schemes are presented for convective flow approximation in reservoir simulation. The methods are compared with slope limited MUSCL and TVD schemes. Standard reservoir simulation schemes employ single-point upstream weighting (first order upwind) for approximation of the convective fluxes when multiple phases or components...
conference paper 2006
document
Bassi, F. (author), Crivellini, A. (author)
Discontinuous Galerkin (DG) methods have proved to be very well suited for the construction of robust high-order numerical schemes on unstructured and possibly non conforming grids for a wide variety of problems. In this paper we consider natural convection flow problems and present a high-order DG method for their numerical solution. The...
conference paper 2006
Searched for: subject%3A%22discontinuous%255C+galerkin%255C+methods%22
(1 - 20 of 26)

Pages

List view
Grid view