A Finite Volume MHD Code in Spherical Coordinates for Background Solar Wind

Abstract

A second-order Godunov-type finite volume method (FVM) to advance the equations of single-fluid solar wind plasma magnetohydrodynamics (MHD) in time has been implemented into a numerical code. This code operates on a three-dimensional (3D) spherical shell with both non-staggered and staggered grids on the overlapping grid system with hexahedral cells of quadrilateral frustum type. By merging geometrical factors in spherical coordinates into the reformulation of fluxes, flux evaluation is made easy to achieve, and thus many numerical schemes with the total variation diminishing (TVD) slope limiters and approximate Roe solvers intended for Cartesian case can follow in the present context of spherical grid described here. At the same time, alternative strategies to ensure a solenoidal magnetic field, such as projection Poisson (PP) solver, hyperbolic divergence cleaning (HDC) method derived from generalized Lagrange multiplier (GLM) formulation of MHD system and constrained transport (CT) method, are employed. In this chapter, an FVM is described exemplarily on a six-component composite grid system by using a minmod limiter for oscillation control. Additionally, an implicit dual time-stepping technique is demonstrated to model the steady state solar wind ambient. Being of second order in space and time, this model is written in FORTRAN language with Message Passing Interface (MPI) parallelization, and validated in modeling the large-scale structure of solar wind from the Sun to Earth process (hereafter called Sun-to-Earth Process MHD model, also STEP-MHD model for brief). To demonstrate the suitability of our code for the simulation of solar wind ambient from the Sun to Earth, selected results from Carrington rotations (CR) during different solar activity phases are presented to show its capability of producing structured solar wind in agreement with observations.