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. Hu, Lijun; Feng, Sebert: An accurate and shock-stable genuinely multidimensional scheme for solving the Euler equations (2021)
  2. Qu, Feng; Sun, Di; Bai, Junqiang: Low-speed modification for the genuinely multidimensional Harten, Lax, van Leer and Einfeldt scheme in curvilinear coordinates (2021)
  3. Sun, Di; Qu, Feng; Liu, Qingsong; Zhong, Jiaxiang: Improvement of the genuinely multidimensional ME-AUSMPW scheme for subsonic flows (2021)
  4. Balsara, Dinshaw S.; Garain, Sudip; Florinski, Vladimir; Boscheri, Walter: An efficient class of WENO schemes with adaptive order for unstructured meshes (2020)
  5. Chandrashekar, Praveen; Kumar, Rakesh: Constraint preserving discontinuous Galerkin method for ideal compressible MHD on 2-D Cartesian grids (2020)
  6. Dumbser, Michael; Fambri, Francesco; Gaburro, Elena; Reinarz, Anne: On GLM curl cleaning for a first order reduction of the CCZ4 formulation of the Einstein field equations (2020)
  7. Liu, Shengping; Shen, Yiqing; Peng, Jun; Zhang, Jun: Two-step weighting method for constructing fourth-order hybrid central WENO scheme (2020)
  8. Montecinos, Gino I.; Balsara, Dinshaw S.: A simplified Cauchy-Kowalewskaya procedure for the local implicit solution of generalized Riemann problems of hyperbolic balance laws (2020)
  9. 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)
  10. Chandrashekar, Praveen: A global divergence conforming DG method for hyperbolic conservation laws with divergence constraint (2019)
  11. Gallardo, José M.; Schneider, Kleiton A.; Castro, Manuel J.: On a class of two-dimensional incomplete Riemann solvers (2019)
  12. Hazra, Arijit; Chandrashekar, Praveen; Balsara, Dinshaw S.: Globally constraint-preserving FR/DG scheme for Maxwell’s equations at all orders (2019)
  13. Kalita, Paragmoni; Sarmah, Sidharth: A new diffusion-regulated flux splitting method for compressible flows (2019)
  14. Qu, Feng; Sun, Di; Bai, Junqiang; Yan, Chao: A genuinely two-dimensional Riemann solver for compressible flows in curvilinear coordinates (2019)
  15. Reyes, Adam; Lee, Dongwook; Graziani, Carlo; Tzeferacos, Petros: A variable high-order shock-capturing finite difference method with GP-WENO (2019)
  16. Simon, Sangeeth; Mandal, J. C.: A simple cure for numerical shock instability in the HLLC Riemann solver (2019)
  17. Wu, Kailiang; Shu, Chi-Wang: Provably positive high-order schemes for ideal magnetohydrodynamics: analysis on general meshes (2019)
  18. 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)
  19. Chen, Shu-Sheng; Yan, Chao; Lin, Bo-Xi; Li, Yan-Su: A new robust carbuncle-free Roe scheme for strong shock (2018)
  20. Felker, Kyle Gerard; Stone, James M.: A fourth-order accurate finite volume method for ideal MHD via upwind constrained transport (2018)

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