An adaptive multiresolution method for ideal magnetohydrodynamics using divergence cleaning with parabolic-hyperbolic correction

TL;DR

This paper introduces an adaptive multiresolution finite volume method for simulating ideal magnetohydrodynamics in 2D, combining divergence cleaning with hyperbolic-parabolic correction to improve efficiency and accuracy.

Contribution

It develops a novel adaptive multiresolution approach with divergence cleaning for ideal MHD, enabling efficient simulations with controlled error and magnetic field divergence.

Findings

Significant CPU time and memory savings demonstrated.

High accuracy maintained compared to fine mesh solutions.

Effective divergence control using GLM with hyperbolic-parabolic correction.

Abstract

We present an adaptive multiresolution method for the numerical simulation of ideal magnetohydrodynamics in two space dimensions. The discretization uses a finite volume scheme based on a Cartesian mesh and an explicit compact Rung-Kutta scheme for time integration. Harten's cell average multiresolution allows to introduce a locally refined spatial mesh while controlling the error. The incompressibility of the magnetic field is controlled by using a Generalized Lagrangian Multiplier (GLM) approach with a mixed hyperbolic-parabolic correction. Different applications to two-dimensional problems illustrate the properties of the method. For each application CPU time and memory savings are reported and numerical aspects of the method are discussed. The accuracy of the adaptive computations is assessed by comparison with reference solutions computed on a regular fine mesh.