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A Compact High Order Space-Time Method for Conservation Laws

Published online by Cambridge University Press:  20 August 2015

Shuangzhang Tu ,
Gordon W. Skelton  and
Qing Pang
Shuangzhang Tu*
Affiliation:
Department of Computer Engineering, Jackson State University, Jackson, MS 39217, USA
Gordon W. Skelton*
Affiliation:
Department of Computer Engineering, Jackson State University, Jackson, MS 39217, USA
Qing Pang*
Affiliation:
Department of Computer Engineering, Jackson State University, Jackson, MS 39217, USA
*
Corresponding author.Email:[email protected]
Email:[email protected]
Email:[email protected]
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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

65M9976M25High order methodspace-time methodcell-vertex scheme (CVS)conservation laws
Type
Research Article
Information
Communications in Computational Physics , Volume 9 , Issue 2 , February 2011 , pp. 441 - 480
Copyright
Copyright © Global Science Press Limited 2011

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