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 280 articles , 1 standard article )

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  1. Berthon, Christophe; Chalons, Christophe; Cornet, Selim; Sperone, Gians: Fully well-balanced, positive and simple approximate Riemann solver for shallow water equations (2016)
  2. Berthon, Christophe; Crestetto, Anaïs; Foucher, Françoise: A well-balanced finite volume scheme for a mixed hyperbolic/parabolic system to model chemotaxis (2016)
  3. Bouchut, François; Lhébrard, Xavier: A 5-wave relaxation solver for the shallow water MHD system (2016)
  4. Cancès, Clément; Mathis, Hélène; Seguin, Nicolas: Error estimate for time-explicit finite volume approximation of strong solutions to systems of conservation laws (2016)
  5. Delestre, Olivier; Ghigo, Arthur R.; Fullana, José-Maria; Lagrée, Pierre-Yves: A shallow water with variable pressure model for blood flow simulation (2016)
  6. Djoufedie, George Noel; Felaco, Elisabetta; Rubino, Bruno; Sampalmieri, Rosella: Convergence of Lax-Friedrichs and Godunov schemes for a nonstrictly hyperbolic system of conservation laws arising in oil recovery (2016)
  7. Schleper, Veronika: A HLL-type Riemann solver for two-phase flow with surface forces and phase transitions (2016)
  8. Abakumov, M.V.: Construction of Godunov-type difference schemes in curvilinear coordinates and an application to spherical coordinates (2015)
  9. Audusse, Emmanuel; Chalons, Christophe; Ung, Philippe: A simple well-balanced and positive numerical scheme for the shallow-water system (2015)
  10. Berthon, Christophe; Dubroca, Bruno; Sangam, Afeintou: An entropy preserving relaxation scheme for ten-moments equations with source terms (2015)
  11. Gomes, Anna Karina Fontes; Domingues, Margarete Oliveira; Schneider, Kai; Mendes, Odim; Deiterding, Ralf: An adaptive multiresolution method for ideal magnetohydrodynamics using divergence cleaning with parabolic-hyperbolic correction (2015)
  12. Lugovsky, A.Yu.; Popov, Yu.P.: Roe-Einfeldt-Osher scheme as applied to the mathematical simulation of accretion disks on parallel computers (2015)
  13. Mahmood, Asif; Wolpert, Robert L.; Pitman, E.Bruce: A physics-based emulator for the simulation of geophysical mass flows (2015)
  14. Maruthi, N.H.; Raghurama Rao, S.V.: An entropy stable central solver for Euler equations (2015)
  15. Mathis, Hélène; Cancès, Clément; Godlewski, Edwige; Seguin, Nicolas: Dynamic model adaptation for multiscale simulation of hyperbolic systems with relaxation (2015)
  16. Zanotti, O.; Dumbser, M.: High order numerical simulations of the Richtmyer-Meshkov instability in a relativistic fluid (2015)
  17. Abakumov, M.V.: Method for the construction of Godunov-type difference schemes in curvilinear coordinates and its application to cylindrical coordinates (2014)
  18. Chertock, Alina; Herty, Michael; Kurganov, Alexander: An Eulerian-Lagrangian method for optimization problems governed by multidimensional nonlinear hyperbolic PDEs (2014)
  19. Martí, M.C.; Mulet, P.: Some techniques for improving the resolution of finite difference component-wise WENO schemes for polydisperse sedimentation models (2014)
  20. Seal, David C.; Güçlü, Yaman; Christlieb, Andrew J.: High-order multiderivative time integrators for hyperbolic conservation laws (2014)

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