Implementation of a non-oscillatory and conservative scheme into magnetohydrodynamic equations
© The Society of Geomagnetism and Earth, Planetary and Space Sciences (SGEPSS); The Seismological Society of Japan; The Volcanological Society of Japan; The Geodetic Society of Japan; The Japanese Society for Planetary Sciences; TERRAPUB. 2009
Received: 21 December 2007
Accepted: 12 February 2009
Published: 31 August 2009
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.