Abstract
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.
Highlights
Magnetohydrodynamic (MHD) simulation techniques are widely used to study various global and macroscopic phenomena in plasmas
Miyoshi and Kusano (2005) recently developed the Harten-Lax-van Leer Discontinuities (HLLD) approximate Riemann solver for the MHD equations
We found that the fast rarefaction waves (FR), slow compound wave (SM), contact discontinuity (CD), and slow shock (SS) are well resolved with Scheme A
Summary
Magnetohydrodynamic (MHD) simulation techniques are widely used to study various global and macroscopic phenomena in plasmas. A new interpolation scheme has recently been developed for the Vlasov equation (Umeda, 2008) This scheme is a non-oscillatory, positivity preserving, and conservative numerical interpolation scheme for solving the linear advection equation. We first extend the non-oscillatory scheme to the general advection equation. In the MOCCT scheme, the van Leer interpolation (van Leer, 1974, 1977) has been generally used to interpolate the magnetic field and velocity to suppress numerical oscillations at discontinuities. To apply the non-oscillatory and MOCCT schemes, we define the left-hand side of Eqs. We briefly review the non-oscillatory scheme and extend it for a general advection equation. In this paper we define a conservation equation (9) as a following non-oscillatory operator, f it +.
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