Riemann solutions for spacetime discontinuous Galerkin methods

Spacetime discontinuous Galerkin finite element methods [1–3] rely on ‘target fluxes’ on elementboundaries that are computed via local one-dimensional Riemann solutions in the direction normal toelement face. In this work, we demonstrate a generalized solution procedure for linearized hyperbolicsystems based on diagonalisation of the governing system of partial differential equations. We showthat source terms do not influence the Riemann solution in the spacetime setting. We provide detailsfor implementation of coordinate transformations and Riemann solutions. Exact Riemann solutionsfor some linear systems of equations are provided as examples. References1. R. ABEDI AND R.B. HABER AND S. THITE AND J. ERICKSON. An h-adaptive spacetime-discontinuous Galerkinmethod for linearized elastodynamics. Revue Européenne des Eléments Finis, 2005.2. S.T. MILLER AND R.B. HABER. A spacetime discontinuous Galerkin method for hyperbolic heat conduction.CMAME 198:2 (2008) 194–209.3. R. ABEDI AND M.A. HAWKER AND R.B. HABER AND K. MATOUŠ. An adaptive spacetime discontinuous Galerkinmethod for cohesive models of elastodynamic fracture. IJNME 81:10 (2010) 1207–1241.