Volume 9, Issue 2
A Compact High Order Space-Time Method for Conservation Laws

Shuangzhang Tu, Gordon W. Skelton & Qing Pang

Commun. Comput. Phys., 9 (2011), pp. 441-480.

Published online: 2011-09

Preview Full PDF 160 1214
Export citation
  • Abstract

This paper presents a novel high-order space-time method for hyperbolic conservation laws. Two important concepts, the staggered space-time mesh of the space-time conservation element/solution element (CE/SE) method and the local discontinuous basis functions of the space-time discontinuous Galerkin (DG) finite element method, are the two key ingredients of the new scheme. The staggered space-time mesh is constructed using the cell-vertex structure of the underlying spatial mesh. The universal definitions of CEs and SEs are independent of the underlying spatial mesh and thus suitable for arbitrarily unstructured meshes. The solution within each physical time step is updated alternately at the cell level and the vertex level. For this solution updating strategy and the DG ingredient, the new scheme here is termed as the discontinuous Galerkin cell-vertex scheme (DG-CVS). The high order of accuracy is achieved by employing high-order Taylor polynomials as the basis functions inside each SE. The present DG-CVS exhibits many advantageous features such as Riemann-solver-free, high-order accuracy, point-implicitness, compactness, and ease of handling boundary conditions. Several numerical tests including the scalar advection equations and compressible Euler equations will demonstrate the performance of the new method.

  • Keywords

  • AMS Subject Headings

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{CiCP-9-441, author = {}, title = {A Compact High Order Space-Time Method for Conservation Laws}, journal = {Communications in Computational Physics}, year = {2011}, volume = {9}, number = {2}, pages = {441--480}, abstract = {

This paper presents a novel high-order space-time method for hyperbolic conservation laws. Two important concepts, the staggered space-time mesh of the space-time conservation element/solution element (CE/SE) method and the local discontinuous basis functions of the space-time discontinuous Galerkin (DG) finite element method, are the two key ingredients of the new scheme. The staggered space-time mesh is constructed using the cell-vertex structure of the underlying spatial mesh. The universal definitions of CEs and SEs are independent of the underlying spatial mesh and thus suitable for arbitrarily unstructured meshes. The solution within each physical time step is updated alternately at the cell level and the vertex level. For this solution updating strategy and the DG ingredient, the new scheme here is termed as the discontinuous Galerkin cell-vertex scheme (DG-CVS). The high order of accuracy is achieved by employing high-order Taylor polynomials as the basis functions inside each SE. The present DG-CVS exhibits many advantageous features such as Riemann-solver-free, high-order accuracy, point-implicitness, compactness, and ease of handling boundary conditions. Several numerical tests including the scalar advection equations and compressible Euler equations will demonstrate the performance of the new method.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.050309.110510a}, url = {http://global-sci.org/intro/article_detail/cicp/7506.html} }
TY - JOUR T1 - A Compact High Order Space-Time Method for Conservation Laws JO - Communications in Computational Physics VL - 2 SP - 441 EP - 480 PY - 2011 DA - 2011/09 SN - 9 DO - http://doi.org/10.4208/cicp.050309.110510a UR - https://global-sci.org/intro/article_detail/cicp/7506.html KW - AB -

This paper presents a novel high-order space-time method for hyperbolic conservation laws. Two important concepts, the staggered space-time mesh of the space-time conservation element/solution element (CE/SE) method and the local discontinuous basis functions of the space-time discontinuous Galerkin (DG) finite element method, are the two key ingredients of the new scheme. The staggered space-time mesh is constructed using the cell-vertex structure of the underlying spatial mesh. The universal definitions of CEs and SEs are independent of the underlying spatial mesh and thus suitable for arbitrarily unstructured meshes. The solution within each physical time step is updated alternately at the cell level and the vertex level. For this solution updating strategy and the DG ingredient, the new scheme here is termed as the discontinuous Galerkin cell-vertex scheme (DG-CVS). The high order of accuracy is achieved by employing high-order Taylor polynomials as the basis functions inside each SE. The present DG-CVS exhibits many advantageous features such as Riemann-solver-free, high-order accuracy, point-implicitness, compactness, and ease of handling boundary conditions. Several numerical tests including the scalar advection equations and compressible Euler equations will demonstrate the performance of the new method.

Shuangzhang Tu, Gordon W. Skelton & Qing Pang. (2020). A Compact High Order Space-Time Method for Conservation Laws. Communications in Computational Physics. 9 (2). 441-480. doi:10.4208/cicp.050309.110510a
Copy to clipboard
The citation has been copied to your clipboard