A Carbuncle Free Roe-Type Solver for the Euler Equations

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

A chapter in Hyperbolic Problems: Theory, Numerics, Applications, 2008, pp 601-608 from Springer

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.

Keywords: Shear Wave; Euler Equation; Shock Front; Riemann Problem; Strong Shock (search for similar items in EconPapers)
Date: 2008
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-540-75712-2_59

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DOI: 10.1007/978-3-540-75712-2_59

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