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 431 articles , 1 standard article )

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  1. Arbogast, Todd; Huang, Chieh-Sen; Zhao, Xikai: Accuracy of WENO and adaptive order WENO reconstructions for solving conservation laws (2018)
  2. 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)
  3. Cai, Zhenning; Torrilhon, Manuel: Numerical simulation of microflows using moment methods with linearized collision operator (2018)
  4. Clain, Stéphane; Loubère, Raphaël; Machado, Gaspar J.: \itA posteriori stabilized sixth-order finite volume scheme for one-dimensional steady-state hyperbolic equations (2018)
  5. 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)
  6. Islam, Asiful; Thornber, Ben: A high-order hybrid turbulence model with implicit large-eddy simulation (2018)
  7. Miyatake, Yuto; Sogabe, Tomohiro; Zhang, Shao-Liang: On the equivalence between SOR-type methods for linear systems and the discrete gradient methods for gradient systems (2018)
  8. Ohwada, Taku; Shibata, Yuki; Kato, Takuma; Nakamura, Taichi: A simple, robust and efficient high-order accurate shock-capturing scheme for compressible flows: towards minimalism (2018)
  9. Pelanti, Marica: Wave structure similarity of the HLLC and Roe Riemann solvers: application to low Mach number preconditioning (2018)
  10. Aissa, Mohamed; Verstraete, Tom; Vuik, Cornelis: Toward a GPU-aware comparison of explicit and implicit CFD simulations on structured meshes (2017)
  11. 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)
  12. Boscheri, Walter; Dumbser, Michael: Arbitrary-Lagrangian-Eulerian discontinuous Galerkin schemes with a posteriori subcell finite volume limiting on moving unstructured meshes (2017)
  13. Boyaval, Sébastien: A finite-volume discretization of viscoelastic Saint-Venant equations for FENE-P fluids (2017)
  14. Caleffi, Valerio; Valiani, Alessandro: Well balancing of the SWE schemes for moving-water steady flows (2017)
  15. Castro, Manuel J.; Ortega, Sergio; Parés, Carlos: Well-balanced methods for the shallow water equations in spherical coordinates (2017)
  16. 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)
  17. Chen, Guoxian; Noelle, Sebastian: A new hydrostatic reconstruction scheme based on subcell reconstructions (2017)
  18. Chen, Tianheng; Shu, Chi-Wang: Entropy stable high order discontinuous Galerkin methods with suitable quadrature rules for hyperbolic conservation laws (2017)
  19. Clain, S.; Figueiredo, J.: The MOOD method for the non-conservative shallow-water system (2017)
  20. Coquel, Frédéric; Hérard, Jean-Marc; Saleh, Khaled: A positive and entropy-satisfying finite volume scheme for the Baer-Nunziato model (2017)

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