Implementation of a non-oscillatory and conservative scheme into magnetohydrodynamic equations

Details Implementation of a non-oscillatory and conservative scheme into magnetohydrodynamic equations Implementation of a non-oscillatory and conservative scheme into magnetohydrodynamic equations

Jul 2009

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2009ep%26s...61..895t&link_type=abstract

Earth, Planets and Space, Volume 61, p. 895-903.

Computer Science

Sound

Scientific paper

We present a magnetohydrodynamic (MHD) simulation technique with a new non-oscillatory and conservative interpolation scheme. Several high-resolution and stable numerical schemes have recently been proposed for solving the MHD equations. To apply the CIP scheme to the hydrodynamic equations, we need to add a certain diffusion term to suppress numerical oscillations at discontinuities. Although the TVD schemes can automatically avoid numerical oscillations, they are not appropriate for profiles with a local maximum or minimum, such as waves. To deal with the above problems, we implement a new non-oscillatory and conservative interpolation scheme in MHD simulations. Several numerical tests are carried out in order to compare our scheme with other recent high-resolution schemes. The numerical tests suggest that the present scheme can follow long-term evolution of both Alfvén waves and compressive shocks. The present scheme has been used for a numerical modeling of Alfvén waves in the solar wind, in which sinusoidal Alfvén waves decay into compressive sound waves that steepen into shocks.

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