Comparison of solvers for the generalized Riemann problem for hyperbolic systems with source terms

  • Authors:

  • G. Montecinos;C. E. Castro;M. Dumbser;E. F. Toro

  • Affiliations:

  • Laboratory of Applied Mathematics, University of Trento, Italy;KlimaCampus Hamburg, University of Hamburg, Germany;Laboratory of Applied Mathematics, University of Trento, Italy;Laboratory of Applied Mathematics, University of Trento, Italy

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2012

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Abstract

We compare four different approximate solvers for the generalized Riemann problem (GRP) for non-linear systems of hyperbolic equations with source terms. The GRP is a special Cauchy problem for a hyperbolic system with source terms whose initial condition is piecewise smooth. We briefly review the four solvers currently available and carry out a systematic assessment of these in terms of accuracy and computational efficiency. These solvers are the building block for constructing high-order numerical schemes of the ADER type for solving the general initial-boundary value problem for inhomogeneous systems in multiple space dimensions, in the frameworks of finite volume and discontinuous Galerkin finite element methods.