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 572 articles , 1 standard article )

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  1. Barsukow, Wasilij: The active flux scheme for nonlinear problems (2021)
  2. Blachère, Florian; Chalons, Christophe; Turpault, Rodolphe: Very high-order asymptotic-preserving schemes for hyperbolic systems of conservation laws with parabolic degeneracy on unstructured meshes (2021)
  3. Chen, Jinqiang; Yu, Peixiang; Ouyang, Hua; Tian, Zhen F.: A novel parallel computing strategy for compact difference schemes with consistent accuracy and dispersion (2021)
  4. Chernykh, Igor; Kulikov, Igor; Tutukov, Alexander: Hydrogen-helium chemical and nuclear galaxy collision: hydrodynamic simulations on AVX-512 supercomputers (2021)
  5. Dong, Jian; Li, Ding Fang: A new second-order modified hydrostatic reconstruction for the shallow water flows with a discontinuous topography (2021)
  6. Hu, Lijun; Feng, Sebert: A robust and contact preserving flux splitting scheme for compressible flows (2021)
  7. Hu, Lijun; Feng, Sebert: An accurate and shock-stable genuinely multidimensional scheme for solving the Euler equations (2021)
  8. Keppens, Rony; Teunissen, Jannis; Xia, Chun; Porth, Oliver: \textttMPI-AMRVAC: a parallel, grid-adaptive PDE toolkit (2021)
  9. Koley, Ujjwal; Ray, Deep; Sarkar, Tanmay: Multilevel Monte Carlo finite difference methods for fractional conservation laws with random data (2021)
  10. Lin, Xue-lei; Ng, Micheal K.; Wathen, Andy: Preconditioners for multilevel Toeplitz linear systems from steady-state and evolutionary advection-diffusion equations (2021)
  11. Berthon, Christophe; Klingenberg, Christian; Zenk, Markus: An all Mach number relaxation upwind scheme (2020)
  12. 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)
  13. Castro, Manuel J.; Parés, Carlos: Well-balanced high-order finite volume methods for systems of balance laws (2020)
  14. Celledoni, Elena; Eidnes, Sølve; Owren, Brynjulf; Ringholm, Torbjørn: Energy-preserving methods on Riemannian manifolds (2020)
  15. Chandrashekar, Praveen; Kumar, Rakesh: Constraint preserving discontinuous Galerkin method for ideal compressible MHD on 2-D Cartesian grids (2020)
  16. Chandrashekar, Praveen; Nkonga, Boniface; Meena, Asha Kumari; Bhole, Ashish: A path conservative finite volume method for a shear shallow water model (2020)
  17. 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)
  18. Chen, Shusheng; Lin, Boxi; Li, Yansu; Yan, Chao: HLLC+: low-Mach shock-stable HLLC-type Riemann solver for all-speed flows (2020)
  19. Dong, Jian: A robust second-order surface reconstruction for shallow water flows with a discontinuous topography and a Manning friction (2020)
  20. 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)

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