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 540 articles , 1 standard article )

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  1. Berthon, Christophe; Klingenberg, Christian; Zenk, Markus: An all Mach number relaxation upwind scheme (2020)
  2. 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)
  3. Castro, Manuel J.; Parés, Carlos: Well-balanced high-order finite volume methods for systems of balance laws (2020)
  4. Celledoni, Elena; Eidnes, Sølve; Owren, Brynjulf; Ringholm, Torbjørn: Energy-preserving methods on Riemannian manifolds (2020)
  5. Chandrashekar, Praveen; Nkonga, Boniface; Meena, Asha Kumari; Bhole, Ashish: A path conservative finite volume method for a shear shallow water model (2020)
  6. 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)
  7. Chen, Shusheng; Lin, Boxi; Li, Yansu; Yan, Chao: HLLC+: low-Mach shock-stable HLLC-type Riemann solver for all-speed flows (2020)
  8. Dong, Jian: A robust second-order surface reconstruction for shallow water flows with a discontinuous topography and a Manning friction (2020)
  9. 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)
  10. Fridrich, David; Liska, Richard; Wendroff, Burton: Cell-centered Lagrangian Lax-Wendroff HLL hybrid scheme in cylindrical geometry (2020)
  11. Ginting, Bobby Minola; Ginting, Herli: Extension of artificial viscosity technique for solving 2D non-hydrostatic shallow water equations (2020)
  12. Gouasmi, Ayoub; Duraisamy, Karthik; Murman, Scott M.; Tadmor, Eitan: A minimum entropy principle in the compressible multicomponent Euler equations (2020)
  13. Guisset, Sébastien: Angular moments models for rarefied gas dynamics. Numerical comparisons with kinetic and Navier-Stokes equations (2020)
  14. 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)
  15. Hu, Zhicheng; Cai, Zhenning; Wang, Yanli: Numerical simulation of microflows using Hermite spectral methods (2020)
  16. Jung, SungKi; Myong, R. S.: A relaxation model for numerical approximations of the multidimensional pressureless gas dynamics system (2020)
  17. Li, Lei; Liu, Jian-Guo: Large time behaviors of upwind schemes and (B)-schemes for Fokker-Planck equations on (\mathbbR) by jump processes (2020)
  18. Liu, Kai; Yang, Jie; Shi, Wei: A new SOR-type iteration method for solving linear systems (2020)
  19. Lu, Xinhua; Mao, Bing; Zhang, Xiaofeng; Ren, Shi: Well-balanced and shock-capturing solving of 3D shallow-water equations involving rapid wetting and drying with a local 2D transition approach (2020)
  20. Maulik, Romit; San, Omer: Numerical assessments of a parametric implicit large eddy simulation model (2020)

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