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Arbitrarily High Order Space-time Method for Conservation Laws on Unstructured Meshes
Final rept. 15 Mar 2008-14 Mar 2010
JACKSON STATE UNIV MS DEPT OF COMPUTER ENGINEERING
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This research 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 elementsolution element CESE 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. Quadrature-free integration is implemented to improve efficiency. The present DG-CVS exhibits many distinct features such as Riemann-solver-free, high-order accuracy in both space and time, point-implicitness, compactness, and ease of handling boundary conditions.
APPROVED FOR PUBLIC RELEASE