Simulating Magnetohydrodynamical Flow with Constrained Transport and Adaptive Mesh Refinement; Algorithms & Tests of the AstroBEAR Code

TL;DR

This paper details the algorithms and testing of the AstroBEAR code, which simulates ideal magnetohydrodynamics using adaptive mesh refinement and constrained transport to accurately maintain magnetic field divergence-free conditions.

Contribution

The paper introduces new algorithms for maintaining divergence-free magnetic fields on adaptive grids within the AstroBEAR code, enhancing simulation accuracy and robustness.

Findings

Code accurately maintains divergence-free magnetic fields.

AstroBEAR demonstrates robustness through various test comparisons.

High-resolution shock capturing schemes improve simulation fidelity.

Abstract

A description is given of the algorithms implemented in the AstroBEAR adaptive mesh refinement code for ideal magnetohydrodynamics. The code provides several high resolution, shock capturing schemes which are constructed to maintain conserved quantities of the flow in a finite volume sense. Divergence free magnetic field topologies are maintained to machine precision by collating the components of the magnetic field on a cell-interface staggered grid and utilizing the constrained transport approach for integrating the induction equations. The maintenance of magnetic field topologies on adaptive grids is achieved using prolongation and restriction operators which preserve the divergence and curl of the magnetic field across co-located grids of different resolution. The robustness and correctness of the code is demonstrated by comparing the numerical solution of various tests with analytical solutions or previously published numerical solutions obtained by other codes.