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

References in zbMATH (referenced in 551 articles , 1 standard article )

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  1. Hu, Lijun; Feng, Sebert: A robust and contact preserving flux splitting scheme for compressible flows (2021)
  2. Keppens, Rony; Teunissen, Jannis; Xia, Chun; Porth, Oliver: \textttMPI-AMRVAC: a parallel, grid-adaptive PDE toolkit (2021)
  3. Berthon, Christophe; Klingenberg, Christian; Zenk, Markus: An all Mach number relaxation upwind scheme (2020)
  4. Bouchut, François; Chalons, Christophe; Guisset, Sébastien: An entropy satisfying two-speed relaxation system for the barotropic Euler equations: application to the numerical approximation of low Mach number flows (2020)
  5. Castro, Manuel J.; Parés, Carlos: Well-balanced high-order finite volume methods for systems of balance laws (2020)
  6. Celledoni, Elena; Eidnes, Sølve; Owren, Brynjulf; Ringholm, Torbjørn: Energy-preserving methods on Riemannian manifolds (2020)
  7. Chandrashekar, Praveen; Kumar, Rakesh: Constraint preserving discontinuous Galerkin method for ideal compressible MHD on 2-D Cartesian grids (2020)
  8. Chandrashekar, Praveen; Nkonga, Boniface; Meena, Asha Kumari; Bhole, Ashish: A path conservative finite volume method for a shear shallow water model (2020)
  9. Chen, Shu-sheng; Cai, Fang-jie; Xue, Hai-chao; Wang, Ning; Yan, Chao: An improved AUSM-family scheme with robustness and accuracy for all Mach number flows (2020)
  10. Chen, Shusheng; Lin, Boxi; Li, Yansu; Yan, Chao: HLLC+: low-Mach shock-stable HLLC-type Riemann solver for all-speed flows (2020)
  11. Dong, Jian: A robust second-order surface reconstruction for shallow water flows with a discontinuous topography and a Manning friction (2020)
  12. Dong, Jian; Li, Ding Fang: A reliable second-order hydrostatic reconstruction for shallow water flows with the friction term and the bed source term (2020)
  13. Fox, Rodney O.; Laurent, Frédérique; Vié, Aymeric: A hyperbolic two-fluid model for compressible flows with arbitrary material-density ratios (2020)
  14. Fridrich, David; Liska, Richard; Wendroff, Burton: Cell-centered Lagrangian Lax-Wendroff HLL hybrid scheme in cylindrical geometry (2020)
  15. Gavrilyuk, Sergey; Nkonga, Boniface; Shyue, Keh-Ming; Truskinovsky, Lev: Stationary shock-like transition fronts in dispersive systems (2020)
  16. Ginting, Bobby Minola; Ginting, Herli: Extension of artificial viscosity technique for solving 2D non-hydrostatic shallow water equations (2020)
  17. Gouasmi, Ayoub; Duraisamy, Karthik; Murman, Scott M.; Tadmor, Eitan: A minimum entropy principle in the compressible multicomponent Euler equations (2020)
  18. Guisset, Sébastien: Angular moments models for rarefied gas dynamics. Numerical comparisons with kinetic and Navier-Stokes equations (2020)
  19. Haines, Brian M.; Keller, D. E.; Marozas, J. A.; McKenty, P. W.; Anderson, K. S.; Collins, T. J. B.; Dai, W. W.; Hall, M. L.; Jones, S.; McKay, M. D. jun.; Rauenzahn, R. M.; Woods, D. N.: Coupling laser physics to radiation-hydrodynamics (2020)
  20. Helluy, Philippe; Hurisse, Olivier; Quibel, Lucie: Simulation of a liquid-vapour compressible flow by a lattice Boltzmann method (2020)

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