Astronomy and Astrophysics – Astronomy
Scientific paper
Sep 2010
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2010aspc..429..258m&link_type=abstract
Numerical Modeling of Space Plasma Flows, Astronum-2009, proceedings of a conference held 29 June through 3 July 2009 in Chamoni
Astronomy and Astrophysics
Astronomy
Scientific paper
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.
Mignone Andrea
Tzeferacos Petros
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