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

¹ Max-Planck-Institut für Sonnensystemforschung, Max Planck Stra β e 2, 37191 Katlenburg-Lindau, Germany
e-mail: hanasoge@mps.mpg.de
² Department of Geosciences, Princeton University, Princeton, NJ 08544, USA
³ Université de Pau et des Pays de l’Adour, CNRS & INRIA Magique-3D, Laboratoire de Modélisation et d’Imagerie en Géosciences UMR 5212, Avenue de l’Université, 64013 Pau Cedex, France
⁴ Institut universitaire de France, 103 boulevard Saint-Michel, 75005 Paris, France

Received: 3 March 2010
Accepted: 29 July 2010

Abstract

Perfectly matched layers are a very efficient way to absorb waves on the outer edges of media. We present a stable convolutional unsplit perfectly matched formulation designed for the linearized stratified Euler equations. 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.