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 339 articles , 1 standard article )

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  1. Aissa, Mohamed; Verstraete, Tom; Vuik, Cornelis: Toward a GPU-aware comparison of explicit and implicit CFD simulations on structured meshes (2017)
  2. Chen, Guoxian; Noelle, Sebastian: A new hydrostatic reconstruction scheme based on subcell reconstructions (2017)
  3. Su, Wei; Tang, Zhenyu; He, Bijiao; Cai, Guobiao: Stable Runge-Kutta discontinuous Galerkin solver for hypersonic rarefied gaseous flow based on 2D Boltzmann kinetic model equations (2017)
  4. Adeleke, Najeem; Adewumi, Michael; Ityokumbul, Thaddeus: Revisiting low-fidelity two-fluid models for gas-solids transport (2016)
  5. Alemi Ardakani, Hamid; Bridges, Thomas J.; Turner, Matthew R.: Shallow-water sloshing in a moving vessel with variable cross-section and wetting-drying using an extension of George’s well-balanced finite volume solver (2016)
  6. Balsara, Dinshaw S.; Montecinos, Gino I.; Toro, Eleuterio F.: Exploring various flux vector splittings for the magnetohydrodynamic system (2016)
  7. Balsara, Dinshaw S.; Vides, Jeaniffer; Gurski, Katharine; Nkonga, Boniface; Dumbser, Michael; Garain, Sudip; Audit, Edouard: A two-dimensional Riemann solver with self-similar sub-structure - alternative formulation based on least squares projection (2016)
  8. Berthon, Christophe; Chalons, Christophe; Cornet, Selim; Sperone, Gians: Fully well-balanced, positive and simple approximate Riemann solver for shallow water equations (2016)
  9. Berthon, Christophe; Crestetto, Anaïs; Foucher, Françoise: A well-balanced finite volume scheme for a mixed hyperbolic/parabolic system to model chemotaxis (2016)
  10. Blachère, F.; Turpault, R.: An admissibility and asymptotic-preserving scheme for systems of conservation laws with source term on 2D unstructured meshes (2016)
  11. Bouchut, François; Lhébrard, Xavier: A 5-wave relaxation solver for the shallow water MHD system (2016)
  12. Cancès, Clément; Mathis, Hélène; Seguin, Nicolas: Error estimate for time-explicit finite volume approximation of strong solutions to systems of conservation laws (2016)
  13. Contarino, Christian; Toro, Eleuterio F.; Montecinos, Gino I.; Borsche, Raul; Kall, Jochen: Junction-generalized Riemann problem for stiff hyperbolic balance laws in networks: an implicit solver and ADER schemes (2016)
  14. Daude, F.; Galon, P.: On the computation of the Baer-Nunziato model using ALE formulation with HLL- and HLLC-type solvers towards fluid-structure interactions (2016)
  15. Delestre, Olivier; Ghigo, Arthur R.; Fullana, José-Maria; Lagrée, Pierre-Yves: A shallow water with variable pressure model for blood flow simulation (2016)
  16. 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)
  17. Dumbser, Michael; Balsara, Dinshaw S.: A new efficient formulation of the HLLEM Riemann solver for general conservative and non-conservative hyperbolic systems (2016)
  18. Guermond, Jean-Luc; Popov, Bojan: Fast estimation from above of the maximum wave speed in the Riemann problem for the Euler equations (2016)
  19. Schleper, Veronika: A HLL-type Riemann solver for two-phase flow with surface forces and phase transitions (2016)
  20. Shen, Hua; Wen, Chih-Yung: A characteristic space-time conservation element and solution element method for conservation laws II. Multidimensional extension (2016)

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