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Unconditionally Stable Explicit Schemes for the Approximation of Conservation Laws

In: Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems

Author

Listed:
  • Christiane Helzel

    (Otto-von-Guericke Universität Magdeburg, Institut für Analysis und Numerik)

  • Gerald Warnecke

    (Otto-von-Guericke Universität Magdeburg, Institut für Analysis und Numerik)

Abstract

We consider explicit schemes for homogeneous conservation laws which satisfy the geometric Courant-Friedrichs-Lewy condition in order to guarantee stability but allow a time step with CFL-number larger than one. A brief overview over existing unconditionally stable schemes for hyperbolic conservation laws is provided, although the focus is on LeVeque’s large time step Godunov scheme. For this scheme we explore the question of entropy consistency for the approximation of one-dimensional scalar conservation laws with convex flux function and describe a possible way to extend the scheme to the two-dimensional case. Numerical calculations and analytical results show that an increase of accuracy can be obtained because the error introduced by the modified evolution step of the large time step Godunov scheme may be less important than the error due to the projection step.

Suggested Citation

  • Christiane Helzel & Gerald Warnecke, 2001. "Unconditionally Stable Explicit Schemes for the Approximation of Conservation Laws," Springer Books, in: Bernold Fiedler (ed.), Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems, pages 775-803, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-56589-2_31
    DOI: 10.1007/978-3-642-56589-2_31
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