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 500 articles , 1 standard article )

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  1. Barsukow, Wasilij: Stationarity preserving schemes for multi-dimensional linear systems (2019)
  2. Berthon, Christophe; Duran, Arnaud; Foucher, Françoise; Saleh, Khaled; Zabsonré, Jean De Dieu: Improvement of the hydrostatic reconstruction scheme to get fully discrete entropy inequalities (2019)
  3. Celledoni, Elena; Puiggalí, Marta Farré; Høiseth, Eirik Hoel; de Diego, David Martín: Energy-preserving integrators applied to nonholonomic systems (2019)
  4. Deininger, Martina; Iben, Uwe; Munz, Claus-Dieter: Coupling of three- and one-dimensional hydraulic flow simulations (2019)
  5. Denissen, I. F. C.; Weinhart, T.; Te Voortwis, A.; Luding, S.; Gray, J. M. N. T.; Thornton, A. R.: Bulbous head formation in bidisperse shallow granular flow over an inclined plane (2019)
  6. Díaz, Manuel Jesús Castro; Kurganov, Alexander; de Luna, Tomás Morales: Path-conservative central-upwind schemes for nonconservative hyperbolic systems (2019)
  7. Escalante, C.; Fernández-Nieto, E. D.; Morales de Luna, T.; Castro, M. J.: An efficient two-layer non-hydrostatic approach for dispersive water waves (2019)
  8. Fleischmann, Nico; Adami, Stefan; Adams, Nikolaus A.: Numerical symmetry-preserving techniques for low-dissipation shock-capturing schemes (2019)
  9. Gebhardt, Cristian Guillermo; Hofmeister, Benedikt; Hente, Christian; Rolfes, Raimund: Nonlinear dynamics of slender structures: a new object-oriented framework (2019)
  10. Haga, Takanori; Kawai, Soshi: On a robust and accurate localized artificial diffusivity scheme for the high-order flux-reconstruction method (2019)
  11. Hornung, H. G.; Martinez Schramm, Jan; Hannemann, Klaus: Hypersonic flow over spherically blunted cone capsules for atmospheric entry. I: The sharp cone and the sphere (2019)
  12. James, François; Lagrée, Pierre-Yves; Le, Minh H.; Legrand, Mathilde: Towards a new friction model for shallow water equations through an interactive viscous layer (2019)
  13. Ke, Guoyi; Guo, Wei: An alternative formulation of discontinous Galerkin schemes for solving Hamilton-Jacobi equations (2019)
  14. Laiu, M. Paul; Hauck, Cory D.: Positivity limiters for filtered spectral approximations of linear kinetic transport equations (2019)
  15. Lin, Jianfang; Abgrall, Rémi; Qiu, Jianxian: High order residual distribution for steady state problems for hyperbolic conservation laws (2019)
  16. Meena, Asha Kumari; Kumar, Harish: Robust numerical schemes for two-fluid ten-moment plasma flow equations (2019)
  17. Rodionov, Alexander V.: Artificial viscosity to cure the shock instability in high-order Godunov-type schemes (2019)
  18. Shadab, Mohammad Afzal; Balsara, Dinshaw; Shyy, Wei; Xu, Kun: Fifth order finite volume WENO in general orthogonally-curvilinear coordinates (2019)
  19. Simon, Sangeeth; Mandal, J. C.: A simple cure for numerical shock instability in the HLLC Riemann solver (2019)
  20. Tiam Kapen, Pascalin; Ghislain, Tchuen: A robust rotated-hybrid Riemann scheme for multidimensional inviscid compressible flows (2019)

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