Multidimensional HLLE Riemann solver: application to Euler and magnetohydrodynamic flows... We also focus on the construction of multidimensionally upwinded electric fields for divergence-free magnetohydrodynamical (MHD) flows. A robust and efficient second order accurate numerical scheme for two and three-dimensional Euler and MHD flows is presented. The scheme is built on the current multidimensional Riemann solver and has been implemented in the author’s RIEMANN code. The number of zones updated per second by this scheme on a modern processor is shown to be cost-competitive with schemes that are based on a one-dimensional Riemann solver. However, the present scheme permits larger timesteps...

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  1. Balsara, Dinshaw S.; Kim, Jinho: A subluminal relativistic magnetohydrodynamics scheme with ADER-WENO predictor and multidimensional Riemann solver-based corrector (2016)
  2. Boscheri, Walter; Dumbser, Michael: An efficient quadrature-free formulation for high order arbitrary-Lagrangian-Eulerian ADER-WENO finite volume schemes on unstructured meshes (2016)
  3. del Razo, M.J.; Morofuji, Y.; Meabon, J.S.; Huber, B.R.; Peskind, E.R.; Banks, W.A.; Mourad, P.D.; LeVeque, R.J.; Cook, D.G.: Computational and in vitro studies of blast-induced blood-brain barrier disruption (2016)
  4. Dumbser, Michael; Balsara, Dinshaw S.: A new efficient formulation of the HLLEM Riemann solver for general conservative and non-conservative hyperbolic systems (2016)
  5. Amano, Takanobu: Divergence-free approximate Riemann solver for the quasi-neutral two-fluid plasma model (2015)
  6. Balsara, Dinshaw S.: Three dimensional HLL Riemann solver for conservation laws on structured meshes; application to Euler and magnetohydrodynamic flows (2015)
  7. Balsara, Dinshaw S.; Dumbser, Michael: Divergence-free MHD on unstructured meshes using high order finite volume schemes based on multidimensional Riemann solvers (2015)
  8. Boscheri, Walter; Dumbser, Michael; Zanotti, Olindo: High order cell-centered Lagrangian-type finite volume schemes with time-accurate local time stepping on unstructured triangular meshes (2015)
  9. Boscheri, Walter; Loubère, Raphaël; Dumbser, Michael: Direct arbitrary-Lagrangian-Eulerian ADER-MOOD finite volume schemes for multidimensional hyperbolic conservation laws (2015)
  10. Guo, Xiaocheng: An extended HLLC Riemann solver for the magneto-hydrodynamics including strong internal magnetic field (2015)
  11. Maruthi, N.H.; Raghurama Rao, S.V.: An entropy stable central solver for Euler equations (2015)
  12. Vides, Jeaniffer; Nkonga, Boniface; Audit, Edouard: A simple two-dimensional extension of the HLL Riemann solver for hyperbolic systems of conservation laws (2015)
  13. Balsara, Dinshaw S.: Multidimensional Riemann problem with self-similar internal structure. Part I: Application to hyperbolic conservation laws on structured meshes (2014)
  14. Balsara, Dinshaw S.; Dumbser, Michael; Abgrall, Remi: Multidimensional HLLC Riemann solver for unstructured meshes -- with application to Euler and MHD flows (2014)
  15. Boscheri, Walter; Balsara, Dinshaw S.; Dumbser, Michael: Lagrangian ADER-WENO finite volume schemes on unstructured triangular meshes based on genuinely multidimensional HLL Riemann solvers (2014)
  16. Castro Díaz, M.J.; Fernández-Nieto, E.D.; Narbona-Reina, G.; de la Asunción, M.: A second order PVM flux limiter method. Application to magnetohydrodynamics and shallow stratified flows (2014)
  17. Dumbser, Michael; Zanotti, Olindo; Loubère, Raphaël; Diot, Steven: \itA posteriori subcell limiting of the discontinuous Galerkin finite element method for hyperbolic conservation laws (2014)
  18. Kim, Jinho; Balsara, Dinshaw S.: A stable HLLC Riemann solver for relativistic magnetohydrodynamics (2014)
  19. Shen, Zhijun; Yan, Wei; Yuan, Guangwei: A robust and contact resolving Riemann solver on unstructured mesh, part II, ALE method (2014)
  20. Shen, Zhijun; Yan, Wei; Yuan, Guangwei: A robust and contact resolving Riemann solver on unstructured mesh, part I, Euler method (2014)

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