Mass Flux Schemes and Connection to Shock Instability

By M. Liou. 2000

208 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Mechanics

View Paper: https://www.semanticscholar.org/paper/16c83fc072458bba9d747bf24e23a8aeba75d271

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In Applied Mathematics

In Computational Mechanics

Citations in the corpus

A NEW MULTI-DIMENSIONAL GENERAL RELATIVISTIC NEUTRINO HYDRODYNAMIC CODE FOR CORE-COLLAPSE SUPERNOVAE. I. METHOD AND CODE TESTS IN SPHERICAL SYMMETRY (2010, background): “…(1994), combining the high resolution of the HLLC solver (Toro et al. 1994; Mignone & Bodo 2005) with the robustness of the HLLE solver (Harten et al. 1983; Einfeldt 1988) against odd–even decoupling near grid-aligned shocks (Quirk 1994; Liou 2000; Kifonidis et al. 2003; Sutherland et al. 2003).”
Spectral (Finite) Volume Method for Conservation Laws on Unstructured Grids. Basic Formulation (2002, methodology): “Meanwhile, the exact Riemann solver used in the Godunov scheme was sometimes replaced by approximate “Riemann solvers” or flux-splitting procedures [29, 34, 36, 42, 45, 48] for better efficiency.”
Spectral (Finite) Volume Method for Conservation Laws on Unstructured Grids (2002, methodology): “Later on, higher order polynomial reconstructions were used to replace the piecewise constant reconstruction, and approximate and more efficient Riemann solvers [21, 25, 29, 31, 35, 37] were employed to replace the exact Riemann solver.”
Non-spherical core collapse supernovae - II. The late-time evolution of globally anisotropic neutrino-driven explosions and their implications for SN 1987 A (2005, background): “Furthermore they ensure the positivity of the scheme, and most important for the present application, the avoidance of the “odd-even-decoupling” and carbuncle phenomena in multidimensional applications (see Liou 2000 for details).”
Two-dimensional hydrodynamic core-collapse supernova simulations with spectral neutrino transport - I. Numerical method and results for a 15 solar mass star (2005, background): “…the vicinity of strong shocks to avoid spurious oscillations (the so-called “odd-even decoupling”, or “carbunkel”, phenomenon) when such shocks are aligned with one of the coordinate directions in multidimensional simulations (Quirk 1994; Liou 2000; Kifonidis et al. 2003; Sutherland et al. 2003).”
Cures for the shock instability: development of a shock-stable Roe scheme (2003, background): “Recently, Liou [9] and Xu [10] presented qualitatively similar analyses.”
A matrix stability analysis of the carbuncle phenomenon (2004, methodology): “This seems in contradiction with the claim of a “self-correcting property of the shock-stable scheme AUSM+” made by Liou [28].”
Non-spherical core collapse supernovae. I. Neutrino-driven convection, Rayleigh-Taylor instabilities, and the formation and propagation of metal clumps (2003, background): “The latter changes are necessary to eliminate the odd-even decoupling instability (Quirk 1994, 1997; Liou 2000), from which the original Colella & Glaz solver suffers (Kifonidis et al. 2000).”
A sequel to AUSM, Part II: AUSM+-up for all speeds (2006, methodology): “Shock instability: carbuncle phenomenon Next, we investigate the so-called shock instability problem [26], first proposed by Quirk [27], in which a plane shock wave is propagating along a channel of constant area.”