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 412 articles , 1 standard article )

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  1. 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)
  2. Cai, Zhenning; Torrilhon, Manuel: Numerical simulation of microflows using moment methods with linearized collision operator (2018)
  3. 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)
  4. Aissa, Mohamed; Verstraete, Tom; Vuik, Cornelis: Toward a GPU-aware comparison of explicit and implicit CFD simulations on structured meshes (2017)
  5. Balsara, Dinshaw S.; Nkonga, Boniface: Multidimensional Riemann problem with self-similar internal structure. Part III: A multidimensional analogue of the HLLI Riemann solver for conservative hyperbolic systems (2017)
  6. Boscheri, Walter; Dumbser, Michael: Arbitrary-Lagrangian-Eulerian discontinuous Galerkin schemes with a posteriori subcell finite volume limiting on moving unstructured meshes (2017)
  7. Boyaval, Sébastien: A finite-volume discretization of viscoelastic Saint-Venant equations for FENE-P fluids (2017)
  8. Caleffi, Valerio; Valiani, Alessandro: Well balancing of the SWE schemes for moving-water steady flows (2017)
  9. Chalons, Christophe; Girardin, Mathieu; Kokh, Samuel: An all-regime Lagrange-projection like scheme for 2D homogeneous models for two-phase flows on unstructured meshes (2017)
  10. Chen, Guoxian; Noelle, Sebastian: A new hydrostatic reconstruction scheme based on subcell reconstructions (2017)
  11. Chen, Tianheng; Shu, Chi-Wang: Entropy stable high order discontinuous Galerkin methods with suitable quadrature rules for hyperbolic conservation laws (2017)
  12. Coquel, Frédéric; Hérard, Jean-Marc; Saleh, Khaled: A positive and entropy-satisfying finite volume scheme for the Baer-Nunziato model (2017)
  13. Etienne, Zachariah B.; Wan, Mew-Bing; Babiuc, Maria C.; McWilliams, Sean T.; Choudhary, Ashok: GiRaFFE: an open-source general relativistic force-free electrodynamics code (2017)
  14. 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)
  15. Kidder, Lawrence E.; Field, Scott E.; Foucart, Francois; Schnetter, Erik; Teukolsky, Saul A.; Bohn, Andy; Deppe, Nils; Diener, Peter; Hébert, François; Lippuner, Jonas; Miller, Jonah; Ott, Christian D.; Scheel, Mark A.; Vincent, Trevor: SpECTRE: A task-based discontinuous Galerkin code for relativistic astrophysics (2017)
  16. Lee, Dongwook; Faller, Hugues; Reyes, Adam: The piecewise cubic method (PCM) for computational fluid dynamics (2017)
  17. Michel-Dansac, Victor; Berthon, Christophe; Clain, Stéphane; Foucher, Françoise: A well-balanced scheme for the shallow-water equations with topography or Manning friction (2017)
  18. Pantano, C.; Saurel, R.; Schmitt, T.: An oscillation free shock-capturing method for compressible van der Waals supercritical fluid flows (2017)
  19. Peluchon, S.; Gallice, G.; Mieussens, L.: A robust implicit-explicit acoustic-transport splitting scheme for two-phase flows (2017)
  20. Perrotta, Andrea; Favini, Bernardo: A second-order finite-volume scheme for Euler equations: kinetic energy preserving and staggering effects (2017)

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