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 451 articles , 1 standard article )

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  1. Wang, Sulin; Xu, Zhengfu: Total variation bounded flux limiters for high order finite difference schemes solving one-dimensional scalar conservation laws (2019)
  2. Arbogast, Todd; Huang, Chieh-Sen; Zhao, Xikai: Accuracy of WENO and adaptive order WENO reconstructions for solving conservation laws (2018)
  3. Betancourt, Fernando; Bürger, Raimund; Chalons, Christophe; Diehl, Stefan; Farås, Sebastian: A random sampling method for a family of temple-class systems of conservation laws (2018)
  4. Cai, Zhenning; Torrilhon, Manuel: Numerical simulation of microflows using moment methods with linearized collision operator (2018)
  5. Castro, Manuel J.; Ortega, Sergio; Parés, Carlos: Reprint of: “Well-balanced methods for the shallow water equations in spherical coordinates” (2018)
  6. Celledoni, Elena; Eidnes, Sølve; Owren, Brynjulf; Ringholm, Torbjørn: Dissipative numerical schemes on Riemannian manifolds with applications to gradient flows (2018)
  7. Chalons, C.; Duvigneau, R.; Fiorini, C.: Sensitivity analysis and numerical diffusion effects for hyperbolic PDE systems with discontinuous solutions. The case of barotropic Euler equations in Lagrangian coordinates (2018)
  8. Chen, Shu-Sheng; Yan, Chao; Lin, Bo-Xi; Li, Yan-Su: A new robust carbuncle-free Roe scheme for strong shock (2018)
  9. Christlieb, Andrew J.; Feng, Xiao; Jiang, Yan; Tang, Qi: A high-order finite difference WENO scheme for ideal magnetohydrodynamics on curvilinear meshes (2018)
  10. Clain, Stéphane; Loubère, Raphaël; Machado, Gaspar J.: \itA posteriori stabilized sixth-order finite volume scheme for one-dimensional steady-state hyperbolic equations (2018)
  11. Coquel, Frédéric; Jin, Shi; Liu, Jian-Guo; Wang, Li: Entropic sub-cell shock capturing schemes via Jin-Xin relaxation and Glimm front sampling for scalar conservation laws (2018)
  12. Fechter, Stefan; Munz, Claus-Dieter; Rohde, Christian; Zeiler, Christoph: Approximate Riemann solver for compressible liquid vapor flow with phase transition and surface tension (2018)
  13. Godunov, S. K.; Klyuchinskii, D. V.; Fortova, S. V.; Shepelev, V. V.: Experimental studies of difference gas dynamics models with shock waves (2018)
  14. Iampietro, D.; Daude, F.; Galon, P.; Hérard, J.-M.: A Mach-sensitive splitting approach for Euler-like systems (2018)
  15. Islam, Asiful; Thornber, Ben: A high-order hybrid turbulence model with implicit large-eddy simulation (2018)
  16. Kulikov, I. M.; Chernykh, I. G.; Glinskiy, B. M.; Protasov, V. A.: An efficient optimization of Hll method for the second generation of Intel Xeon Phi processor (2018)
  17. Li, Wanai; Pan, Jianhua; Ren, Yu-Xin: The discontinuous Galerkin spectral element methods for compressible flows on two-dimensional mixed grids (2018)
  18. Mach, Patryk; Piróg, Michał; Font, José A.: Relativistic low angular momentum accretion: long time evolution of hydrodynamical inviscid flows (2018)
  19. Miyatake, Yuto; Sogabe, Tomohiro; Zhang, Shao-Liang: On the equivalence between SOR-type methods for linear systems and the discrete gradient methods for gradient systems (2018)
  20. Ohwada, Taku; Shibata, Yuki; Kato, Takuma; Nakamura, Taichi: A simple, robust and efficient high-order accurate shock-capturing scheme for compressible flows: towards minimalism (2018)

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