HLLE

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 582 articles , 1 standard article )

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  1. Barsukow, Wasilij: The active flux scheme for nonlinear problems (2021)
  2. 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)
  3. Chen, Jinqiang; Yu, Peixiang; Ouyang, Hua; Tian, Zhen F.: A novel parallel computing strategy for compact difference schemes with consistent accuracy and dispersion (2021)
  4. Chernykh, Igor; Kulikov, Igor; Tutukov, Alexander: Hydrogen-helium chemical and nuclear galaxy collision: hydrodynamic simulations on AVX-512 supercomputers (2021)
  5. Dong, Jian; Li, Ding Fang: A new second-order modified hydrostatic reconstruction for the shallow water flows with a discontinuous topography (2021)
  6. Hornung, H. G.: Shock detachment and drag in hypersonic flow over wedges and circular cylinders (2021)
  7. Hu, Lijun; Feng, Sebert: An accurate and shock-stable genuinely multidimensional scheme for solving the Euler equations (2021)
  8. Hu, Lijun; Feng, Sebert: A robust and contact preserving flux splitting scheme for compressible flows (2021)
  9. Kazhyken, Kazbek; Videman, Juha; Dawson, Clint: Discontinuous Galerkin methods for a dispersive wave hydro-sediment-morphodynamic model (2021)
  10. Kazhyken, Kazbek; Videman, Juha; Dawson, Clint: Discontinuous Galerkin methods for a dispersive wave hydro-morphodynamic model with bed-load transport (2021)
  11. Keppens, Rony; Teunissen, Jannis; Xia, Chun; Porth, Oliver: \textttMPI-AMRVAC: a parallel, grid-adaptive PDE toolkit (2021)
  12. Koley, Ujjwal; Ray, Deep; Sarkar, Tanmay: Multilevel Monte Carlo finite difference methods for fractional conservation laws with random data (2021)
  13. Lin, Xue-lei; Ng, Micheal K.; Wathen, Andy: Preconditioners for multilevel Toeplitz linear systems from steady-state and evolutionary advection-diffusion equations (2021)
  14. Moore, Brian E.: Exponential integrators based on discrete gradients for linearly damped/driven Poisson systems (2021)
  15. Pimentel-García, Ernesto; Parés, Carlos; Castro, Manuel J.; Koellermeier, Julian: On the efficient implementation of PVM methods and simple Riemann solvers. Application to the Roe method for large hyperbolic systems (2021)
  16. Berthon, Christophe; Klingenberg, Christian; Zenk, Markus: An all Mach number relaxation upwind scheme (2020)
  17. Bouchut, François; Chalons, Christophe; Guisset, Sébastien: An entropy satisfying two-speed relaxation system for the barotropic Euler equations: application to the numerical approximation of low Mach number flows (2020)
  18. Castro, Manuel J.; Parés, Carlos: Well-balanced high-order finite volume methods for systems of balance laws (2020)
  19. Celledoni, Elena; Eidnes, Sølve; Owren, Brynjulf; Ringholm, Torbjørn: Energy-preserving methods on Riemannian manifolds (2020)
  20. Chandrashekar, Praveen; Kumar, Rakesh: Constraint preserving discontinuous Galerkin method for ideal compressible MHD on 2-D Cartesian grids (2020)

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