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 386 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. Boyaval, Sébastien: A finite-volume discretization of viscoelastic Saint-Venant equations for FENE-P fluids (2017)
  3. Caleffi, Valerio; Valiani, Alessandro: Well balancing of the SWE schemes for moving-water steady flows (2017)
  4. Chen, Guoxian; Noelle, Sebastian: A new hydrostatic reconstruction scheme based on subcell reconstructions (2017)
  5. Goutal, Nicole; Le, Minh-Hoang; Ung, Philippe: A Godunov-type scheme for shallow water equations dedicated to simulations of overland flows on stepped slopes (2017)
  6. Lee, Dongwook; Faller, Hugues; Reyes, Adam: The piecewise cubic method (PCM) for computational fluid dynamics (2017)
  7. Peluchon, S.; Gallice, G.; Mieussens, L.: A robust implicit-explicit acoustic-transport splitting scheme for two-phase flows (2017)
  8. 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)
  9. Tavelli, Maurizio; Dumbser, Michael: A pressure-based semi-implicit space-time discontinuous Galerkin method on staggered unstructured meshes for the solution of the compressible Navier-Stokes equations at all Mach numbers (2017)
  10. Wong, Man Long; Lele, Sanjiva K.: High-order localized dissipation weighted compact nonlinear scheme for shock- and interface-capturing in compressible flows (2017)
  11. Adeleke, Najeem; Adewumi, Michael; Ityokumbul, Thaddeus: Revisiting low-fidelity two-fluid models for gas-solids transport (2016)
  12. 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)
  13. Balsara, Dinshaw S.; Montecinos, Gino I.; Toro, Eleuterio F.: Exploring various flux vector splittings for the magnetohydrodynamic system (2016)
  14. 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)
  15. Berthon, Christophe; Chalons, Christophe: A fully well-balanced, positive and entropy-satisfying Godunov-type method for the shallow-water equations (2016)
  16. Berthon, Christophe; Chalons, Christophe; Cornet, Selim; Sperone, Gians: Fully well-balanced, positive and simple approximate Riemann solver for shallow water equations (2016)
  17. Berthon, Christophe; Crestetto, Anaïs; Foucher, Françoise: A well-balanced finite volume scheme for a mixed hyperbolic/parabolic system to model chemotaxis (2016)
  18. Blachère, F.; Turpault, R.: An admissibility and asymptotic-preserving scheme for systems of conservation laws with source term on 2D unstructured meshes (2016)
  19. Bouchut, François; Lhébrard, Xavier: A 5-wave relaxation solver for the shallow water MHD system (2016)
  20. Cancès, Clément; Mathis, Hélène; Seguin, Nicolas: Error estimate for time-explicit finite volume approximation of strong solutions to systems of conservation laws (2016)

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