Three-dimensional MHD high-resolution computations with CWENO employing adaptive mesh refinement Until recently, numerical simulations of discontinuities in highly super-Alfvénic plasmas have been severely limited by comparatively crude resolution and accuracy. Significant progress in the numerical simulation of such plasmas was achieved with the recently implemented Central Weighted Essentially Non-Oscillatory (CWENO) scheme. Combining this technique with that of adaptive mesh refinement (AMR), we have developed a third-order numerical scheme, which is able to efficiently capture strong gradients on spatial scales being small compared to the overall scale of the plasma system considered. Here, we first describe important algorithmic aspects of the scheme as well as the physics included in it. Second, we present the results of various performance tests. And, third, we illustrate its application to `real world problems’ using the example of the dynamics of a Sedov-type explosion

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  1. Hatori, Tomoharu; Ito, Atsushi M.; Nunami, Masanori; Usui, Hideyuki; Miura, Hideaki: Level-by-level artificial viscosity and visualization for MHD simulation with adaptive mesh refinement (2016)
  2. Ivan, L.; De Sterck, H.; Susanto, A.; Groth, C.P.T.: High-order central ENO finite-volume scheme for hyperbolic conservation laws on three-dimensional cubed-sphere grids (2015)
  3. Susanto, A.; Ivan, L.; De Sterck, H.; Groth, C.P.T.: High-order central ENO finite-volume scheme for ideal MHD (2013)
  4. Guo, Yan; Liu, Ruxun: Characteristic-based finite volume scheme for 1D Euler equations (2009)
  5. Zahran, Yousef Hashem: An efficient WENO scheme for solving hyperbolic conservation laws (2009)
  6. Cai, Li; Feng, Jianhu; Xie, Wenxian: An efficient ghost fluid method for compressible multifluids in Lagrangian coordinate (2008)
  7. Havlík, P.; Liska, R.: Comparison of several finite difference methods for magnetohydrodynamics in 1D and 2D (2008)
  8. Zhou, Jun; Cai, Li; Zhou, Feng-Qi: New high-resolution scheme for three-dimensional nonlinear hyperbolic conservation laws (2008)
  9. Kissmann, R.; Grauer, R.: A low dissipation essentially non-oscillatory central scheme (2007)
  10. Xie, Wenxian; Cai, Li; Feng, Jianhu: Tracking entropy wave in ideal MHD equations by weighted ghost fluid method (2007)
  11. Zhou, Jun; Cai, Li; Feng, Jianhu; Xie, Wenxian: Numerical simulation for two-phase flows using hybrid scheme (2007)
  12. Caleffi, V.; Valiani, A.; Bernini, A.: Fourth-order balanced source term treatment in central WENO schemes for shallow water equations (2006)
  13. Chen, Jianzhong; Shi, Zhongke: Application of a fourth-order relaxation scheme to hyperbolic systems of conservation laws (2006)
  14. Chen, Jian-Zhong; Shi, Zhong-Ke: Solution of 2D shallow water equations by genuinely multidimensional semi-discrete central scheme (2006)
  15. Feng, Jianhu; Cai, Li; Xie, Wenxian: CWENO-type central-upwind schemes for multidimensional Saint-Venant system of shallow water equations (2006)
  16. Kunik, Matthias; Qamar, Shamsul; Warnecke, Gerald: A high order gas kinetic method for the relativistic Euler equations (2006)
  17. Teyssier, Romain; Fromang, Sébastien; Dormy, Emmanuel: Kinematic dynamos using constrained transport with high-order Godunov schemes and adaptive mesh refinement (2006)
  18. Tóth, Gábor; De Zeeuw, Darren L.; Gombosi, Tamas I.; Powell, Kenneth G.: A parallel explicit/implicit time stepping scheme on block-adaptive grids (2006)
  19. Cai, Li; Feng, Jian-Hu; Xie, Wen-Xian: A CWENO-type central-upwind scheme for ideal MHD equations (2005)
  20. Ketcheson, David I.; Robinson, Allen C.: On the practical importance of the SSP property for Runge-Kutta time integrators for some common Godunov-type schemes (2005)

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