RIEMANN

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 58 articles )

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  1. Balsara, Dinshaw S.; Käppeli, Roger: Von Neumann stability analysis of globally constraint-preserving DGTD and PNPM schemes for the Maxwell equations using multidimensional Riemann solvers (2019)
  2. Chandrashekar, Praveen: A global divergence conforming DG method for hyperbolic conservation laws with divergence constraint (2019)
  3. Simon, Sangeeth; Mandal, J. C.: A simple cure for numerical shock instability in the HLLC Riemann solver (2019)
  4. Wu, Kailiang; Shu, Chi-Wang: Provably positive high-order schemes for ideal magnetohydrodynamics: analysis on general meshes (2019)
  5. 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)
  6. Chen, Shu-Sheng; Yan, Chao; Lin, Bo-Xi; Li, Yan-Su: A new robust carbuncle-free Roe scheme for strong shock (2018)
  7. Felker, Kyle Gerard; Stone, James M.: A fourth-order accurate finite volume method for ideal MHD via upwind constrained transport (2018)
  8. Fu, Pei; Li, Fengyan; Xu, Yan: Globally divergence-free discontinuous Galerkin methods for ideal magnetohydrodynamic equations (2018)
  9. Yang, Yun; Feng, Xue-Shang; Jiang, Chao-Wei: An upwind CESE scheme for 2D and 3D MHD numerical simulation in general curvilinear coordinates (2018)
  10. Balsara, Dinshaw S.; Käppeli, Roger: Von Neumann stability analysis of globally divergence-free RKDG schemes for the induction equation using multidimensional Riemann solvers (2017)
  11. 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)
  12. 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)
  13. Basting, Melanie; Kuzmin, Dmitri: An FCT finite element scheme for ideal MHD equations in 1D and 2D (2017)
  14. Caleffi, Valerio; Valiani, Alessandro: Well balancing of the SWE schemes for moving-water steady flows (2017)
  15. Lee, Dongwook; Faller, Hugues; Reyes, Adam: The piecewise cubic method (PCM) for computational fluid dynamics (2017)
  16. Yang, Yun; Feng, Xue-Shang; Jiang, Chao-Wei: A high-order CESE scheme with a new divergence-free method for MHD numerical simulation (2017)
  17. 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)
  18. Balsara, Dinshaw S.; Kim, Jinho: A subluminal relativistic magnetohydrodynamics scheme with ADER-WENO predictor and multidimensional Riemann solver-based corrector (2016)
  19. Balsara, Dinshaw S.; Montecinos, Gino I.; Toro, Eleuterio F.: Exploring various flux vector splittings for the magnetohydrodynamic system (2016)
  20. 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)

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