A Shock Stabilization of the HLLC Riemann Solver for the Carbuncle Instability

• Published in: Journal of scientific computing Vol. 98; no. 2; p. 33
• Main Authors: Baumgart, Alexandra, Jones, Samuel W., Edelmann, Philipp V. F., Dolence, Joshua C.
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.02.2024; Springer Nature B.V; Springer
• Subjects: Algorithms; carbuncle phenomenon; Computational Mathematics and Numerical Analysis; Eigenvalues; Finite volume method; HLLC Riemann solver; Investigations; Mathematical and Computational Engineering; Mathematical and Computational Physics; Mathematics; MATHEMATICS AND COMPUTING; Mathematics and Statistics; Physics; Riemann solver; Sensors; shock instability; Simulation; Stability; Theoretical; Velocity; Viscosity; 76L05; HLLC Riemann solver; Carbuncle phenomenon; 76N06; Shock instability; 76M12
• ISSN: 0885-7474; 1573-7691
• DOI: 10.1007/s10915-023-02419-8

The HLLC approximate Riemann solver improves upon the HLL Riemann solver by resolving contact discontinuities. This is a particularly desirable property for multi-material codes in which problems usually contain material interfaces. However, the HLLC solver is known to suffer from the carbuncle phenomenon, a numerical instability most apparent at grid-aligned shocks in multi-dimensional simulations. Many problems of interest, including high energy-density physics applications, require the accurate resolution of both material interfaces and hydrodynamic shocks. A variety of methods have been developed to cure this instability, with varying degrees of complexity. The objective of this work is to describe a simple approach to modify the HLLC Riemann solver and prevent the carbuncle instability. The method is then demonstrated for assorted two-dimensional test problems known to exhibit the shock instability. The performance of the new solver is compared with that of the standard HLL and HLLC Riemann solvers.