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A Carbuncle Free Roe-Type Solver for the Euler Equations

In: Hyperbolic Problems: Theory, Numerics, Applications

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  • F. Kemm

    (Universität Cottbus (BTU), Inst. f. Ang. Math. u. Wiss. Rechnen Brandenburgische Technische)

Abstract

Based on the idea of the HLLEM scheme, we propose a novel ansatz to cure the well known carbuncle instability. Instead of testing all neighboring cells for strong shocks we test the Riemann problem for contact and shear waves. As an indicator we suggest the residual of the Rankine–Hugoniot condition for the linear waves. By using known approaches, we can apply a well tempered amount of viscosity for the contact and shear waves of the Roe and HLLEM methods. The resulting Riemann solver approximates contact and shear waves exactly. However, according to the chosen value of a parameter, the Carbuncle phenomenon can be completely avoided.

Suggested Citation

  • F. Kemm, 2008. "A Carbuncle Free Roe-Type Solver for the Euler Equations," Springer Books, in: Sylvie Benzoni-Gavage & Denis Serre (ed.), Hyperbolic Problems: Theory, Numerics, Applications, pages 601-608, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-75712-2_59
    DOI: 10.1007/978-3-540-75712-2_59
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