Development of a magnetohydrodynamic simulation code satisfying the solenoidal magnetic field condition

Abstract

We have developed a new magnetohydrodynamic (MHD) simulation code that automatically satisfies the solenoidal magnetic field ( B) property ∇ ⋅ B = 0 . We use the vector potential ( A) instead of the magnetic field itself in the magnetohydrodynamic equation. To solve the advection term, we adopt a Rational-CIP algorithm in the simulation code. The non-advection terms are solved by the 4th order Runge–Kutta method for time and 4th order central difference for space in a regular grid system. Code assessments are carried out to evaluate the properties of the developed code. A remarkable feature of the new code is the description of Alfven wave propagation with less numerical dispersion. After the code assessments, we apply the code to a global simulation of the planet Mercury's magnetosphere. Fundamental structures of the magnetosphere are successfully reproduced.