An absorbing boundary formulation for the stratified, linearized, ideal MHD equations based on an unsplit, convolutional perfectly matched layer

TL;DR

This paper develops a stable, convolutional, unsplit perfectly matched layer (PML) method for absorbing waves in stratified, linearized ideal MHD equations, with applications to solar wave propagation modeling.

Contribution

It introduces a novel PML formulation tailored for stratified MHD equations, enhancing wave absorption efficiency and stability in numerical simulations.

Findings

The PML method is numerically stable over many wave periods.

The approach effectively absorbs outgoing waves in stratified MHD models.

Application to solar wave propagation demonstrates practical utility.

Abstract

Perfectly matched layers are a very efficient and accurate way to absorb waves in media. We present a stable convolutional unsplit perfectly matched formulation designed for the linearized stratified Euler equations. However, the technique as applied to the Magneto-hydrodynamic (MHD) equations requires the use of a sponge, which, despite placing the perfectly matched status in question, is still highly efficient at absorbing outgoing waves. We study solutions of the equations in the backdrop of models of linearized wave propagation in the Sun. We test the numerical stability of the schemes by integrating the equations over a large number of wave periods.