A New MHD Code with Adaptive Mesh Refinement and Parallelization for Astrophysics

TL;DR

This paper introduces MAP, a new Fortran-based MHD simulation code with adaptive mesh refinement and MPI parallelization, offering multiple numerical schemes and advanced algorithms for accurate astrophysical modeling.

Contribution

The paper presents a novel MHD code, MAP, integrating AMR, MPI parallelization, multiple numerical schemes, and algorithms for non-ideal effects, enhancing simulation accuracy and efficiency.

Findings

Implemented multiple second-order numerical schemes.

Achieved high-resolution simulations with hierarchical AMR.

Reduced magnetic divergence errors using EGLM MHD equations.

Abstract

A new code, named MAP, is written in Fortran language for magnetohydrodynamics (MHD) calculation with the adaptive mesh refinement (AMR) and Message Passing Interface (MPI) parallelization. There are several optional numerical schemes for computing the MHD part, namely, modified Mac Cormack Scheme (MMC), Lax-Friedrichs scheme (LF) and weighted essentially non-oscillatory (WENO) scheme. All of them are second order, two-step, component-wise schemes for hyperbolic conservative equations. The total variation diminishing (TVD) limiters and approximate Riemann solvers are also equipped. A high resolution can be achieved by the hierarchical block-structured AMR mesh. We use the extended generalized Lagrange multiplier (EGLM) MHD equations to reduce the non-divergence free error produced by the scheme in the magnetic induction equation. The numerical algorithms for the non-ideal terms, e.g., the resistivity and the thermal conduction, are also equipped in the MAP code. The details of the AMR and MPI algorithms are described in the paper.