Temporal Substepping Scheme for Magnetohydrodynamics with Cell-based Adaptive Mesh Refinement on Staggered Grid

TL;DR

This paper introduces a novel numerical algorithm for magnetohydrodynamics that maintains divergence-free magnetic fields, supports adaptive mesh refinement, and employs temporal substepping without interpolation or coupling between grid levels.

Contribution

It presents a new constrained transport-based method that efficiently handles resolution changes directly on staggered grids with adaptive refinement and temporal substepping.

Findings

Preserves divergence-free magnetic fields during simulations.

Supports cell-based adaptive mesh refinement without interpolation.

Enables temporal substepping on staggered grids.

Abstract

We present a new algorithm for numerical magnetohydrodynamics on staggered meshes preserving $\nabla \cdot B = 0$. Our algorithm is based on the constrained transport method and supports both cell-based adaptive mesh refinement and temporal substepping. We handle resolution changes directly on the logically Cartesian grid without needing interpolation or projection between nested or neighboring grids, nor coupling the solution between refinement levels.