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 527 articles , 1 standard article )

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  1. Castro, Manuel J.; Parés, Carlos: Well-balanced high-order finite volume methods for systems of balance laws (2020)
  2. Celledoni, Elena; Eidnes, Sølve; Owren, Brynjulf; Ringholm, Torbjørn: Energy-preserving methods on Riemannian manifolds (2020)
  3. Chen, Shu-sheng; Cai, Fang-jie; Xue, Hai-chao; Wang, Ning; Yan, Chao: An improved AUSM-family scheme with robustness and accuracy for all Mach number flows (2020)
  4. Dong, Jian: A robust second-order surface reconstruction for shallow water flows with a discontinuous topography and a Manning friction (2020)
  5. Dong, Jian; Li, Ding Fang: A reliable second-order hydrostatic reconstruction for shallow water flows with the friction term and the bed source term (2020)
  6. Ginting, Bobby Minola; Ginting, Herli: Extension of artificial viscosity technique for solving 2D non-hydrostatic shallow water equations (2020)
  7. Gouasmi, Ayoub; Duraisamy, Karthik; Murman, Scott M.; Tadmor, Eitan: A minimum entropy principle in the compressible multicomponent Euler equations (2020)
  8. Haines, Brian M.; Keller, D. E.; Marozas, J. A.; McKenty, P. W.; Anderson, K. S.; Collins, T. J. B.; Dai, W. W.; Hall, M. L.; Jones, S.; McKay, M. D. jun.; Rauenzahn, R. M.; Woods, D. N.: Coupling laser physics to radiation-hydrodynamics (2020)
  9. Hu, Zhicheng; Cai, Zhenning; Wang, Yanli: Numerical simulation of microflows using Hermite spectral methods (2020)
  10. Lu, Xinhua; Mao, Bing; Zhang, Xiaofeng; Ren, Shi: Well-balanced and shock-capturing solving of 3D shallow-water equations involving rapid wetting and drying with a local 2D transition approach (2020)
  11. Maulik, Romit; San, Omer: Numerical assessments of a parametric implicit large eddy simulation model (2020)
  12. Pereira, F. S.; Grinstein, F. F.; Israel, D.: Effect of the numerical discretization scheme in shock-driven turbulent mixing simulations (2020)
  13. Trojak, Will; Watson, Rob; Scillitoe, Ashley; Tucker, Paul G.: Effect of mesh quality on flux reconstruction in multi-dimensions (2020)
  14. Barsukow, Wasilij: Stationarity preserving schemes for multi-dimensional linear systems (2019)
  15. 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)
  16. Celledoni, Elena; Puiggalí, Marta Farré; Høiseth, Eirik Hoel; de Diego, David Martín: Energy-preserving integrators applied to nonholonomic systems (2019)
  17. Deininger, Martina; Iben, Uwe; Munz, Claus-Dieter: Coupling of three- and one-dimensional hydraulic flow simulations (2019)
  18. 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)
  19. Díaz, Manuel Jesús Castro; Kurganov, Alexander; de Luna, Tomás Morales: Path-conservative central-upwind schemes for nonconservative hyperbolic systems (2019)
  20. 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)

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