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...

References in zbMATH (referenced in 9 articles )

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  1. Boscheri, Walter; Dumbser, Michael: An efficient quadrature-free formulation for high order arbitrary-Lagrangian-Eulerian ADER-WENO finite volume schemes on unstructured meshes (2016)
  2. 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)
  3. Maruthi, N.H.; Raghurama Rao, S.V.: An entropy stable central solver for Euler equations (2015)
  4. Balsara, Dinshaw S.; Meyer, Chad; Dumbser, Michael; Du, Huijing; Xu, Zhiliang: Efficient implementation of ADER schemes for Euler and magnetohydrodynamical flows on structured meshes -- speed comparisons with Runge-Kutta methods (2013)
  5. Dumbser, Michael; Boscheri, Walter: High-order unstructured Lagrangian one-step WENO finite volume schemes for non-conservative hyperbolic systems: applications to compressible multi-phase flows (2013)
  6. Balsara, Dinshaw S.: A two-dimensional HLLC Riemann solver for conservation laws: application to Euler and magnetohydrodynamic flows (2012)
  7. Capdeville, G.: A multi-dimensional HLL-Riemann solver for Euler equations of gas dynamics (2011)
  8. Capdeville, G.: A high-order multi-dimensional HLL-Riemann solver for non-linear Euler equations (2011)
  9. Balsara, Dinshaw S.: Multidimensional HLLE Riemann solver: application to Euler and magnetohydrodynamic flows (2010)