An ideal compressible magnetohydrodynamic solver with parallel block-structured adaptive mesh refinement

Abstract

We present an adaptive parallel solver for the numerical simulation of ideal magnetohydrodynamics in two and three space dimensions. The discretisation uses a finite volume scheme based on a Cartesian mesh and an explicit compact Runge–Kutta scheme for time integration. Numerically, a generalized Lagrangian multiplier approach with a mixed hyperbolic-parabolic correction is used to guarantee a control on the incompressibility of the magnetic field. We implement the solver in the AMROC (Adaptive Mesh Refinement in Object-oriented C++) framework that uses a structured adaptive mesh refinement (SAMR) method discretisation-independent and is fully parallelised for distributed memory systems. Moreover, AMROC is a modular framework providing manageability, extensibility and efficiency. In this paper, we give an overview of the ideal magnetohydrodynamics solver developed in this framework and its capabilities. We also include an example of this solver’s verification with other codes and its numerical and computational performance.