HLLE
The HLLE[3] (Harten, Lax, van Leer and Einfeldt) solver is an approximate solution to the Riemann problem, which is only based on the integral form of the conservation laws and the largest and smallest signal velocities at the interface. The stability and robustness of the HLLE solver is closely related to the signal velocities and a single central average state, as proposed by Einfeldt in the original paper. The description of the HLLE scheme in the book mentioned below is incomplete and partially wrong. The reader is referred to the original paper. Actually, the HLLE scheme is based on a new stability theory for discontinuities in fluids, which was never published. HLLC solver The HLLC (Harten-Lax-van Leer-Contact) solver was introduced by Toro.[4] It restores the missing Rarefaction wave by some estimates, like linearisations, these can be simple but also more advanced exists like using the Roe average velocity for the middle wave speed. They are quite robust and efficient but somewhat more diffusive.[5] https://math.nyu.edu/ jbu200/E1GODF.F
Keywords for this software
References in zbMATH (referenced in 638 articles , 1 standard article )
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