Finite volume schemes with equilibrium type discretization of source terms for scalar conservation laws

  • Authors:

  • Ramaz Botchorishvili;Olivier Pironneau

  • Affiliations:

  • VIAM, Tbilisi State University, 2 University Street, Tbilisi 380043, Georgia and Laboratoire d'Analyse Numérique, Université Pierre et Marie Curie, France;University of Paris VI, Analyse Numerique, 175 Rue du Chevaleret, Paris F-75013, France

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2003

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Abstract

We develop here a new class of finite volume schemes on unstructured meshes for scalar conservation laws with stiff source terms. The schemes are of equilibrium type, hence with uniform bounds on approximate solutions, valid in cell entropy inequalities and exact for some equilibrium states. Convergence is investigated in the framework of kinetic schemes. Numerical tests show high computational efficiency and a significant advantage over standard cell centered discretization of source terms. Equilibrium type schemes produce accurate results even on test problems for which the standard approach fails. For some numerical tests they exhibit exponential type convergence rate. In two of our numerical tests an equilibrium type scheme with 441 nodes on a triangular mesh is more accurate than a standard scheme with 50002 grid points.