# On the verification of adaptive three-dimensional multiresolution computations of the magnetohydrodynamic equations

## TL;DR

This paper presents a new 3D magnetohydrodynamic solver with adaptive multiresolution capabilities, enabling efficient and accurate simulations of plasma dynamics by focusing computational effort on regions with complex structures.

## Contribution

Introduction of a divergence-cleaning 3D MHD solver within the CARMEN code utilizing adaptive multiresolution for improved efficiency and accuracy.

## Key findings

- The new solver conserves physical quantities effectively.
- Adaptive mesh refinement improves resolution in critical regions.
- Comparison shows competitive performance with FLASH code.

## Abstract

Magnetohydrodynamics is an important tool to study the dynamics of plasma Space Physics. In this context, we introduce a three-dimensional magnetohydrodynamic solver with divergence-cleaning in the adaptive multiresolution CARMEN code. The numerical scheme is based on a finite volume discretization that ensures the conservation of physical quantities. The adaptive multiresolution approach allows for automatic identification of local structures in the numerical solution and thus provides an adaptive mesh refined only in regions where the solution needs more improved resolution. We assess the three-dimensional magnetohydrodynamic CARMEN code and compare its results with the ones from the well-known FLASH code.