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Open Access

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

Earth, Planets and Space200961:BF03353200

https://doi.org/10.1186/BF03353200

Received: 21 December 2007

Accepted: 12 February 2009

Published: 31 August 2009

Abstract

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.

Key words

MHDnumerical schemehyperbolic equationconservative scheme

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