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| 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. |
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