Physics – Plasma Physics
Scientific paper
Dec 2006
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2006agufmsm21c0275m&link_type=abstract
American Geophysical Union, Fall Meeting 2006, abstract #SM21C-0275
Physics
Plasma Physics
7800 Space Plasma Physics, 7833 Mathematical And Numerical Techniques (0500, 3200), 7836 Mhd Waves And Instabilities (2149, 2752, 6050), 7851 Shock Waves (4455), 7900 Space Weather
Scientific paper
In space plasmas, shocks and discontinuities are often generated. Although shock capturing schemes are required, straightforward multi-dimensional extension of the shock capturing MHD solvers sometimes leads an inappropriate numerical solution that breaks the solenoidal condition of the magnetic field. Therefore, various divergence cleaning methods for multi-dimensional MHD solvers have been proposed so far. Since the projection method can satisfy the solenoidal condition with arbitrary precision by solving Poisson equation with arbitrary precision numerically, the solution of the projection method has been used as a reference solution for other divergence cleaning methods. In low beta plasmas, however, the positivity of the pressure may not be preserved because the corrected magnetic energy density can become larger than the total energy density. Also, the numerical solution is susceptible to odd-even decoupling, if the magnetic divergence is completely cleaned up in the discrete level. In this study, only the perpendicular component of the magnetic field on cell boundary, rather than the magnetic field vector in the cell, is corrected by the projection method. Therefore, the magnetic energy in the cell is simply computed from the original MHD solvers with no modification, and a property of the original solvers may be succeeded to. Furthermore, in this method, odd-even decoupling can be avoided while satisfying the solenoidal condition in the discrete level. Numerical tests show that the present method gives a solution quite similar to the original projection method though the magnetic field in itself is not corrected. Moreover, even in low beta case, the present method seems to be more robust compared with the original projection method, because it may retain the positivity-preserving property of the original solver.
Kusano Kanya
Miyoshi Takahiro
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