Back to Volume
Paper: High Order Finite Difference Schemes for MHD
Volume: 429, Numerical Modeling of Space Plasma Flows, Astronum-2009
Page: 258
Authors: Mignone, A.; Tzeferacos, P.
Abstract: We investigate and compare third- as well as fifth-order accurate finite difference schemes for the explicit numerical solution of the MHD equations. The proposed numerical methods are based on a cell-centered approach where flow variables are evolved as point values located at the zone center and the divergence-free condition is enforced using the hyperbolic/parabolic ansatz of Dedner’s (J. Comput. Phys. 175 (2002) 645-673). This avoids expensive elliptic divergence cleaning steps and the additional complexities required by staggered mesh algorithms still resulting in robust, cost-effective schemes. Chosen reconstruction techniques include recently improved weighted essentially non-oscillatory (WENO), monotonicity preserving (MP) as well as slope-limited polynomial reconstruction schemes. The resulting methods provide highly accurate solutions in smooth regions of the flow avoiding clipping at extrema and provide sharp non-oscillatory transitions at discontinuities.
Back to Volume