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A General Perfectly Matched Layer Model for Hyperbolic-Parabolic Systems

Appelö, Daniel and Hagstrom, Thomas (2009) A General Perfectly Matched Layer Model for Hyperbolic-Parabolic Systems. SIAM Journal on Scientific Computing, 31 (5). pp. 3301-3323. ISSN 1064-8275. http://resolver.caltech.edu/CaltechAUTHORS:20091218-115910674

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Abstract

This paper describes a very general absorbing layer model for hyperbolic-parabolic systems of partial differential equations. For linear systems with constant coefficients it is shown that the model possesses the perfect matching property, i.e., it is a perfectly matched layer (PML). The model is applied to two linear systems: a linear wave equation with a viscous damping term and the linearized Navier–Stokes equations. The resulting perfectly matched layer for the viscous wave equation is proved to be stable. The paper also presents how the model can be used to construct an absorbing layer for the full compressible Navier–Stokes equations. For all three applications, numerical experiments are presented. Especially for the linear problems, the results are very promising. In one experiment, where the performance of a “hyperbolic PML” and the new hyperbolic-parabolic PML is compared for a hyperbolic-parabolic system, an improvement of six orders of magnitude is observed. For the compressible Navier–Stokes equations results obtained with the presented layer are competitive with existing methods.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1137/080713951 DOIUNSPECIFIED
Additional Information:© 2009 Society for Industrial and Applied Mathematics. Received January 22, 2008; accepted May 8, 2009; published August 5, 2009. This work performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52- 07NA27344.
Funders:
Funding AgencyGrant Number
U.S. Department of Energy by Lawrence Livermore National Laboratory DE-AC52-07NA27344
Subject Keywords:perfectly matched layers; hyperbolic-parabolic systems
Issue or Number:5
Classification Code:AMS subject classifications. 35L45, 35B35.
Record Number:CaltechAUTHORS:20091218-115910674
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20091218-115910674
Official Citation:A General Perfectly Matched Layer Model for Hyperbolic-Parabolic Systems Daniel Appelo and Thomas Hagstrom, SIAM J. Sci. Comput. 31, 3301 (2009), DOI:10.1137/080713951
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:17001
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:06 Jan 2010 00:29
Last Modified:29 Mar 2014 03:31

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