Volume 2, Issue 2
A Slope Limiting Procedure in Discontinuous Galerkin Finite Element Method for Gasdynamics Applications

S. Tu & S. Aliabadi

Int. J. Numer. Anal. Mod., 2 (2005), pp. 163-178.

Published online: 2005-02

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  • Abstract

In this paper we demonstrate the performance of a slope limiting procedure combined with a discontinuous Galerkin (DG) finite element solver for 2D compressible Euler equations. The slope limiter can be categorized into van Albada type and is differentiable. This slope limiter is modified from a similar limiter used in finite volume solvers to suit the needs of the DC solver. The gradient in an element is limited using the weighted average of the face gradients. The face gradients are obtained from the area-weighted average of the gradient on both sides of the faces. The slope limiting process is very suitable for meshes discretized by triangle elements. The HLLC (Harten, Lax and van Leer) or the local Lax-Friedrich (LLF) flux functions is used to compute the interface fluxes in the DG formulation. The second order TVD Runge-Kutta scheme is employed for the time integration. The numerical examples including transonic, supersonic and hypersonic flows show that the current slope limiting process together with the DG solver is able to remove overshoots and undershoots around high gradient regions while preserving the high accuracy of the DC method. The convergence histories of all examples demonstrate that the limiting process does not stall convergence to steady state as many other slope limiters do.

  • Keywords

discontinuous Galerkin (DC), slope limiting and 2D inviscid compressible flows.

  • AMS Subject Headings

35L65, 76M10, 76N15

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-2-163, author = {Tu , S. and Aliabadi , S.}, title = {A Slope Limiting Procedure in Discontinuous Galerkin Finite Element Method for Gasdynamics Applications}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2005}, volume = {2}, number = {2}, pages = {163--178}, abstract = {

In this paper we demonstrate the performance of a slope limiting procedure combined with a discontinuous Galerkin (DG) finite element solver for 2D compressible Euler equations. The slope limiter can be categorized into van Albada type and is differentiable. This slope limiter is modified from a similar limiter used in finite volume solvers to suit the needs of the DC solver. The gradient in an element is limited using the weighted average of the face gradients. The face gradients are obtained from the area-weighted average of the gradient on both sides of the faces. The slope limiting process is very suitable for meshes discretized by triangle elements. The HLLC (Harten, Lax and van Leer) or the local Lax-Friedrich (LLF) flux functions is used to compute the interface fluxes in the DG formulation. The second order TVD Runge-Kutta scheme is employed for the time integration. The numerical examples including transonic, supersonic and hypersonic flows show that the current slope limiting process together with the DG solver is able to remove overshoots and undershoots around high gradient regions while preserving the high accuracy of the DC method. The convergence histories of all examples demonstrate that the limiting process does not stall convergence to steady state as many other slope limiters do.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/927.html} }
TY - JOUR T1 - A Slope Limiting Procedure in Discontinuous Galerkin Finite Element Method for Gasdynamics Applications AU - Tu , S. AU - Aliabadi , S. JO - International Journal of Numerical Analysis and Modeling VL - 2 SP - 163 EP - 178 PY - 2005 DA - 2005/02 SN - 2 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/927.html KW - discontinuous Galerkin (DC), slope limiting and 2D inviscid compressible flows. AB -

In this paper we demonstrate the performance of a slope limiting procedure combined with a discontinuous Galerkin (DG) finite element solver for 2D compressible Euler equations. The slope limiter can be categorized into van Albada type and is differentiable. This slope limiter is modified from a similar limiter used in finite volume solvers to suit the needs of the DC solver. The gradient in an element is limited using the weighted average of the face gradients. The face gradients are obtained from the area-weighted average of the gradient on both sides of the faces. The slope limiting process is very suitable for meshes discretized by triangle elements. The HLLC (Harten, Lax and van Leer) or the local Lax-Friedrich (LLF) flux functions is used to compute the interface fluxes in the DG formulation. The second order TVD Runge-Kutta scheme is employed for the time integration. The numerical examples including transonic, supersonic and hypersonic flows show that the current slope limiting process together with the DG solver is able to remove overshoots and undershoots around high gradient regions while preserving the high accuracy of the DC method. The convergence histories of all examples demonstrate that the limiting process does not stall convergence to steady state as many other slope limiters do.

S. Tu & S. Aliabadi. (1970). A Slope Limiting Procedure in Discontinuous Galerkin Finite Element Method for Gasdynamics Applications. International Journal of Numerical Analysis and Modeling. 2 (2). 163-178. doi:
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