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.; Garain, Sudip; Taflove, Allen; Montecinos, Gino: Computational electrodynamics in material media with constraint-preservation, multidimensional Riemann solvers and sub-cell resolution. II: Higher order FVTD schemes (2018)
  2. Chen, Shu-Sheng; Yan, Chao; Lin, Bo-Xi; Li, Yan-Su: A new robust carbuncle-free Roe scheme for strong shock (2018)
  3. Fu, Pei; Li, Fengyan; Xu, Yan: Globally divergence-free discontinuous Galerkin methods for ideal magnetohydrodynamic equations (2018)
  4. Balsara, Dinshaw S.; Käppeli, Roger: Von Neumann stability analysis of globally divergence-free RKDG schemes for the induction equation using multidimensional Riemann solvers (2017)
  5. Balsara, Dinshaw S.; Nkonga, Boniface: Multidimensional Riemann problem with self-similar internal structure. Part III: A multidimensional analogue of the HLLI Riemann solver for conservative hyperbolic systems (2017)
  6. Balsara, Dinshaw S.; Taflove, Allen; Garain, Sudip; Montecinos, Gino: Computational electrodynamics in material media with constraint-preservation, multidimensional Riemann solvers and sub-cell resolution. I: Second-order FVTD schemes. (2017)
  7. Caleffi, Valerio; Valiani, Alessandro: Well balancing of the SWE schemes for moving-water steady flows (2017)
  8. Lee, Dongwook; Faller, Hugues; Reyes, Adam: The piecewise cubic method (PCM) for computational fluid dynamics (2017)
  9. Yang, Yun; Feng, Xue-Shang; Jiang, Chao-Wei: A high-order CESE scheme with a new divergence-free method for MHD numerical simulation (2017)
  10. 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)
  11. Balsara, Dinshaw S.; Kim, Jinho: A subluminal relativistic magnetohydrodynamics scheme with ADER-WENO predictor and multidimensional Riemann solver-based corrector (2016)
  12. Balsara, Dinshaw S.; Montecinos, Gino I.; Toro, Eleuterio F.: Exploring various flux vector splittings for the magnetohydrodynamic system (2016)
  13. 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)
  14. Borah, Kalpajyoti; Natarajan, Ganesh; Dass, Anoop K.: A novel second-order flux splitting for ideal magnetohydrodynamics (2016)
  15. Boscheri, Walter; Dumbser, Michael: An efficient quadrature-free formulation for high order arbitrary-Lagrangian-Eulerian ADER-WENO finite volume schemes on unstructured meshes (2016)
  16. 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)
  17. Dumbser, Michael; Balsara, Dinshaw S.: A new efficient formulation of the HLLEM Riemann solver for general conservative and non-conservative hyperbolic systems (2016)
  18. Dumbser, Michael; Casulli, Vincenzo: A conservative, weakly nonlinear semi-implicit finite volume scheme for the compressible Navier-Stokes equations with general equation of state (2016)
  19. Dumbser, Michael; Loubère, Raphaël: A simple robust and accurate \textitaposteriori sub-cell finite volume limiter for the discontinuous Galerkin method on unstructured meshes (2016)
  20. Kulikov, Igor; Vorobyov, Eduard: Using the PPML approach for constructing a low-dissipation, operator-splitting scheme for numerical simulations of hydrodynamic flows (2016)

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