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. Zhou, Boxiao; Qu, Feng; Liu, Qingsong; Sun, Di; Bai, Junqiang: A study of multidimensional fifth-order WENO method for genuinely two-dimensional Riemann solver (2022)
  2. Boscheri, W.; Dumbser, M.; Ioriatti, M.; Peshkov, I.; Romenski, E.: A structure-preserving staggered semi-implicit finite volume scheme for continuum mechanics (2021)
  3. Chiocchetti, Simone; Peshkov, Ilya; Gavrilyuk, Sergey; Dumbser, Michael: High order ADER schemes and GLM curl cleaning for a first order hyperbolic formulation of compressible flow with surface tension (2021)
  4. Han Veiga, Maria; Velasco-Romero, David A.; Wenger, Quentin; Teyssier, Romain: An arbitrary high-order spectral difference method for the induction equation (2021)
  5. Hu, Lijun; Feng, Sebert: An accurate and shock-stable genuinely multidimensional scheme for solving the Euler equations (2021)
  6. Lee, Youngjun; Lee, Dongwook: A single-step third-order temporal discretization with Jacobian-free and Hessian-free formulations for finite difference methods (2021)
  7. Mignone, A.; Del Zanna, L.: Systematic construction of upwind constrained transport schemes for MHD (2021)
  8. Qu, Feng; Sun, Di; Bai, Junqiang: Low-speed modification for the genuinely multidimensional Harten, Lax, van Leer and Einfeldt scheme in curvilinear coordinates (2021)
  9. Schneider, Kleiton A.; Gallardo, José M.; Balsara, Dinshaw S.; Nkonga, Boniface; Parés, Carlos: Multidimensional approximate Riemann solvers for hyperbolic nonconservative systems. Applications to shallow water systems (2021)
  10. Sun, Di; Qu, Feng; Liu, Qingsong; Zhong, Jiaxiang: Improvement of the genuinely multidimensional ME-AUSMPW scheme for subsonic flows (2021)
  11. Zhou, Boxiao; Qu, Feng; Sun, Di; Wang, Zirui; Bai, Junqiang: A study of higher-order reconstruction methods for genuinely two-dimensional Riemann solver (2021)
  12. Balsara, Dinshaw S.; Garain, Sudip; Florinski, Vladimir; Boscheri, Walter: An efficient class of WENO schemes with adaptive order for unstructured meshes (2020)
  13. Chandrashekar, Praveen; Kumar, Rakesh: Constraint preserving discontinuous Galerkin method for ideal compressible MHD on 2-D Cartesian grids (2020)
  14. 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)
  15. Hu, Lijun; Yuan, Li; Zhao, Kunlei: Development of accurate and robust genuinely two-dimensional HLL-type Riemann solver for compressible flows (2020)
  16. Käppeli, Roger; Balsara, Dinshaw S.; Chandrashekar, Praveen; Hazra, Arijit: Optimal, globally constraint-preserving, (\mathrmDG(TD)^2) schemes for computational electrodynamics based on two-derivative Runge-Kutta timestepping and multidimensional generalized Riemann problem solvers -- a von Neumann stability analysis (2020)
  17. Kuzmin, Dmitri; Klyushnev, Nikita: Limiting and divergence cleaning for continuous finite element discretizations of the MHD equations (2020)
  18. Liu, Shengping; Shen, Yiqing; Peng, Jun; Zhang, Jun: Two-step weighting method for constructing fourth-order hybrid central WENO scheme (2020)
  19. 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)
  20. Qu, Feng; Sun, Di; Zhou, Boxiao; Bai, Junqiang: Self-similar structures based genuinely two-dimensional Riemann solvers in curvilinear coordinates (2020)

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