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 309 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. Abe, Yoshiaki; Haga, Takanori; Nonomura, Taku; Fujii, Kozo: On the freestream preservation of high-order conservative flux-reconstruction schemes (2015)
  10. Audusse, Emmanuel; Chalons, Christophe; Ung, Philippe: A simple well-balanced and positive numerical scheme for the shallow-water system (2015)
  11. Balsara, Dinshaw S.: Three dimensional HLL Riemann solver for conservation laws on structured meshes; application to Euler and magnetohydrodynamic flows (2015)
  12. Balsara, Dinshaw S.; Dumbser, Michael: Multidimensional Riemann problem with self-similar internal structure. Part II: Application to hyperbolic conservation laws on unstructured meshes (2015)
  13. Berthon, Christophe; Dubroca, Bruno; Sangam, Afeintou: An entropy preserving relaxation scheme for ten-moments equations with source terms (2015)
  14. 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)
  15. Guo, Xiaocheng: An extended HLLC Riemann solver for the magneto-hydrodynamics including strong internal magnetic field (2015)
  16. Henry de Frahan, Marc T.; Varadan, Sreenivas; Johnsen, Eric: A new limiting procedure for discontinuous Galerkin methods applied to compressible multiphase flows with shocks and interfaces (2015)
  17. Le Touze, C.; Murrone, A.; Guillard, H.: Multislope MUSCL method for general unstructured meshes (2015)
  18. Lugovsky, A.Yu.; Popov, Yu.P.: Roe-Einfeldt-Osher scheme as applied to the mathematical simulation of accretion disks on parallel computers (2015)
  19. Mahmood, Asif; Wolpert, Robert L.; Pitman, E.Bruce: A physics-based emulator for the simulation of geophysical mass flows (2015)
  20. Maruthi, N.H.; Raghurama Rao, S.V.: An entropy stable central solver for Euler equations (2015)

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