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.; Amano, Takanobu; Garain, Sudip; Kim, Jinho: A high-order relativistic two-fluid electrodynamic scheme with consistent reconstruction of electromagnetic fields and a multidimensional Riemann solver for electromagnetism (2016)
  2. Balsara, Dinshaw S.; Kim, Jinho: A subluminal relativistic magnetohydrodynamics scheme with ADER-WENO predictor and multidimensional Riemann solver-based corrector (2016)
  3. Balsara, Dinshaw S.; Montecinos, Gino I.; Toro, Eleuterio F.: Exploring various flux vector splittings for the magnetohydrodynamic system (2016)
  4. Balsara, Dinshaw S.; Vides, Jeaniffer; Gurski, Katharine; Nkonga, Boniface; Dumbser, Michael; Garain, Sudip; Audit, Edouard: A two-dimensional Riemann solver with self-similar sub-structure - alternative formulation based on least squares projection (2016)
  5. Borah, Kalpajyoti; Natarajan, Ganesh; Dass, Anoop K.: A novel second-order flux splitting for ideal magnetohydrodynamics (2016)
  6. Boscheri, Walter; Dumbser, Michael: An efficient quadrature-free formulation for high order arbitrary-Lagrangian-Eulerian ADER-WENO finite volume schemes on unstructured meshes (2016)
  7. 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)
  8. Dumbser, Michael; Balsara, Dinshaw S.: A new efficient formulation of the HLLEM Riemann solver for general conservative and non-conservative hyperbolic systems (2016)
  9. Dumbser, Michael; Loubère, Raphaël: A simple robust and accurate \ita posteriori sub-cell finite volume limiter for the discontinuous Galerkin method on unstructured meshes (2016)
  10. Kulikov, Igor; Vorobyov, Eduard: Using the PPML approach for constructing a low-dissipation, operator-splitting scheme for numerical simulations of hydrodynamic flows (2016)
  11. Shen, Zhijun; Yan, Wei; Yuan, Guangwei: A robust HLLC-type Riemann solver for strong shock (2016)
  12. Yang, Yan; Wan, Minping; Shi, Yipeng; Yang, Kun; Chen, Shiyi: A hybrid scheme for compressible magnetohydrodynamic turbulence (2016)
  13. Amano, Takanobu: Divergence-free approximate Riemann solver for the quasi-neutral two-fluid plasma model (2015)
  14. Balsara, Dinshaw S.: Three dimensional HLL Riemann solver for conservation laws on structured meshes; application to Euler and magnetohydrodynamic flows (2015)
  15. Balsara, Dinshaw S.; Dumbser, Michael: Divergence-free MHD on unstructured meshes using high order finite volume schemes based on multidimensional Riemann solvers (2015)
  16. Balsara, Dinshaw S.; Dumbser, Michael: Multidimensional Riemann problem with self-similar internal structure. Part II: Application to hyperbolic conservation laws on unstructured meshes (2015)
  17. 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)
  18. Boscheri, Walter; Loubère, Raphaël; Dumbser, Michael: Direct arbitrary-Lagrangian-Eulerian ADER-MOOD finite volume schemes for multidimensional hyperbolic conservation laws (2015)
  19. Guo, Xiaocheng: An extended HLLC Riemann solver for the magneto-hydrodynamics including strong internal magnetic field (2015)
  20. Maruthi, N.H.; Raghurama Rao, S.V.: An entropy stable central solver for Euler equations (2015)

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