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 638 articles , 1 standard article )

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  1. Alldredge, Graham; Frank, Martin; Kusch, Jonas; McClarren, Ryan: A realizable filtered intrusive polynomial moment method (2022)
  2. Kolluru, Ramesh; Raghavendra, N. V.; Raghurama Rao, S. V.; Sekhar, G. N.: Simple and robust contact-discontinuity capturing central algorithms for high speed compressible flows (2022)
  3. Kusch, Jonas; Schlachter, Louisa: Oscillation mitigation of hyperbolicity-preserving intrusive uncertainty quantification methods for systems of conservation laws (2022)
  4. Wakimura, Hiro; Takagi, Shinichi; Xiao, Feng: Symmetry-preserving enforcement of low-dissipation method based on boundary variation diminishing principle (2022)
  5. Xie, Wenjia; Tian, Zhengyu; Zhang, Ye; Yu, Hang; Ren, Weijie: A unified construction of all-speed HLL-type schemes for hypersonic heating computations (2022)
  6. Xu, Renyi; Borthwick, Alistair G. L.; Ma, Hongbo; Xu, Bo: Godunov-type large time step scheme for shallow water equations with bed-slope source term (2022)
  7. Barsukow, Wasilij: The active flux scheme for nonlinear problems (2021)
  8. Berberich, Jonas P.; Käppeli, Roger; Chandrashekar, Praveen; Klingenberg, Christian: High order discretely well-balanced methods for arbitrary hydrostatic atmospheres (2021)
  9. Biswas, Tirtha Roy; Dey, Subhasish; Sen, Dhrubajyoti: Modeling positive surge propagation in open channels using the Serre-Green-Naghdi equations (2021)
  10. Blachère, Florian; Chalons, Christophe; Turpault, Rodolphe: Very high-order asymptotic-preserving schemes for hyperbolic systems of conservation laws with parabolic degeneracy on unstructured meshes (2021)
  11. Brull, Stéphane; Dubroca, Bruno; Lhébrard, Xavier: Modelling and entropy satisfying relaxation scheme for the nonconservative bitemperature Euler system with transverse magnetic field (2021)
  12. Bulteau, Solène; Badsi, Mehdi; Berthon, Christophe; Bessemoulin-Chatard, Marianne: A fully well-balanced and asymptotic preserving scheme for the shallow-water equations with a generalized Manning friction source term (2021)
  13. Busto, S.; Río-Martín, L.; Vázquez-Cendón, M. E.; Dumbser, M.: A semi-implicit hybrid finite volume/finite element scheme for all Mach number flows on staggered unstructured meshes (2021)
  14. Chan, Agnes; Gallice, Gérard; Loubère, Raphaël; Maire, Pierre-Henri: Positivity preserving and entropy consistent approximate Riemann solvers dedicated to the high-order MOOD-based finite volume discretization of Lagrangian and Eulerian gas dynamics (2021)
  15. Chen, Jinqiang; Yu, Peixiang; Ouyang, Hua; Tian, Zhen F.: A novel parallel computing strategy for compact difference schemes with consistent accuracy and dispersion (2021)
  16. Chernykh, Igor; Kulikov, Igor; Tutukov, Alexander: Hydrogen-helium chemical and nuclear galaxy collision: hydrodynamic simulations on AVX-512 supercomputers (2021)
  17. Chiapolino, Alexandre; Fraysse, François; Saurel, Richard: A method to solve Hamilton-Jacobi type equation on unstructured meshes (2021)
  18. Chiapolino, Alexandre; Saurel, Richard; Toro, Eleuterio: Investigation of Riemann solver with internal reconstruction (RSIR) for the Euler equations (2021)
  19. Del Grosso, A.; Chalons, C.: Second-order well-balanced Lagrange-projection schemes for blood flow equations (2021)
  20. Dong, Jian; Li, Ding Fang: A new second-order modified hydrostatic reconstruction for the shallow water flows with a discontinuous topography (2021)

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