A matrix stability analysis of the carbuncle phenomenon

DOI10.1016/j.jcp.2003.12.013zbMath1079.76607OpenAlexW2119854869MaRDI QIDQ598169

Jean-Marc Moschetta, Michael Dumbser, Jérémie Gressier

Publication date: 6 August 2004

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jcp.2003.12.013

zbMATH Keywords

Riemann solversStability analysisCarbuncle phenomenonNumerical shock structureShock instabilityUpwind schemes

Mathematics Subject Classification ID

Shock waves and blast waves in fluid mechanics (76L05) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12)

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Uses Software

• AUSMPW+

Cites Work

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• On Godunov-type methods near low densities
• High resolution schemes for hyperbolic conservation laws
• Direct simulation methods for compressible inviscid ideal-gas flow
• Multidimensional dissipation for upwind schemes: Stability and applications to gas dynamics
• Restoration of the contact surface in the HLL-Riemann solver
• Dissipation additions to flux-difference splitting
• A low-diffusion flux-splitting scheme for Navier-Stokes calculations
• Mass flux schemes and connection to shock instability
• Positivity of flux vector splitting schemes
• An entropy fix for multi-dimensional upwind residual distribution schemes
• Dissipative mechanism in Godunov-type schemes
• A kinetic theory solution method for the Navier–Stokes equations
• A contribution to the great Riemann solver debate
• An Accurate and Robust Flux Splitting Scheme for Shock and Contact Discontinuities
• On the Choice of Wavespeeds for the HLLC Riemann Solver
• Shock wave instability and the carbuncle phenomenon: same intrinsic origin?
• Numerical instabilities in upwind methods: Analysis and cures for the ``carbuncle phenomenon
• Methods for the accurate computations of hypersonic flows. I: AUSMPW+scheme