Physics – Fluid Dynamics
Scientific paper
Feb 2007
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2007gapfd.101...37w&link_type=abstract
Geophysical and Astrophysical Fluid Dynamics, vol. 100, Issue 1, p.37-61
Physics
Fluid Dynamics
2
Magnetohydrodynamics, Essentially Non-Oscillatory Scheme
Scientific paper
We present a high order accurate weighted essentially non-oscillatory (WENO) finite difference scheme for solving the equations of incompressible fluid dynamics and magnetohydrodynamics (MHD). This scheme is a direct extension of a WENO scheme that has been successfully applied to compressible fluids, with or without magnetic fields. A fractional time-step method is used to enforce the incompressibility condition. Two basic elements of the WENO scheme, upwinding and wave decomposition, are shown to be important in solving the incompressible systems. Numerical results demonstrate that the scheme performs well for one-dimensional Riemann problems, a two-dimensional double-shear flow problem, and the two-dimensional Orszag-Tang MHD vortex system. They establish that the WENO code is numerical stable even when there are no explicit dissipation terms. It can handle discontinuous data and attain converged results with a high order of accuracy.
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