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Complete Radiation Boundary Conditions for Convective Waves

Published online by Cambridge University Press:  20 August 2015

Thomas Hagstrom ,
Eliane Bécache ,
Dan Givoli  and
Kurt Stein
Thomas Hagstrom*
Affiliation:
Dept. of Mathematics, Southern Methodist University, Dallas, TX 75275, USA
Eliane Bécache*
Affiliation:
Propagation des Ondes, Etude Mathématique et Simulation (POEMS), INRIA, Domaine de Voluceau-Rocquencourt, BP 105, 78153 Le Chesnay Cedex, France
Dan Givoli*
Affiliation:
Dept. of Aerospace Engineering, Technion, Haifa 32000, Israel
Kurt Stein*
Affiliation:
Dept. of Mathematics, Southern Methodist University, Dallas, TX 75275, USA
*
Corresponding author.Email:[email protected]
Email address:[email protected]
Email address:[email protected]
Email address:[email protected]
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Abstract

Local approximate radiation boundary conditions of optimal efficiency for the convective wave equation and the linearized Euler equations in waveguide geometry are formulated, analyzed, and tested. The results extend and improve for the convective case the general formulation of high-order local radiation boundary condition sequences for anisotropic scalar equations developed in [4].

Keywords

65M1235L5035C15Radiation boundary conditionsconvective waves
Type
Research Article
Information
Communications in Computational Physics , Volume 11 , Issue 2 , February 2012 , pp. 610 - 628
Copyright
Copyright © Global Science Press Limited 2012

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References

[1]Atassi, O.. Nonreflecting boundary conditions for the time-dependent convective wave equation in a duct. J. Comput. Phys., 197:737–758, 2004.CrossRefGoogle Scholar
[2]Atassi, O. and Galán, J.. Implementation of nonreflecting boundary conditions for the nonlinear Euler equations. J. Comput. Phys., 227:1643–1662, 2008.Google Scholar
[3]Bécache, E., Fauqueux, S., and Joly, P.. Stability of perfectly matched layers, group velocities, and anisotropic waves. J. Comput. Phys., 188:399–433, 2003.Google Scholar
[4]Bécache, E., Givoli, D., and Hagstrom, T.. High-order Absorbing Boundary Conditions for anisotropic and convective wave equations. J. Comput. Phys., 229:1099–1129, 2010.Google Scholar
[5]Bayliss, A. and Turkel, E.. Far field boundary conditions for compressible flows. J. Comput. Phys., 48:182–199, 1982.Google Scholar
[6]Diaz, J. and Joly, P.. Stabilized perfectly matched layer for advective acoustics. In Cohen, G., Heikkola, E., Joly, P., and Neittaanmäki, P., editors, Mathematical and Numerical Aspects of Wave Propagation Phenomena, pages 115–119. Springer, 2003.Google Scholar
[7]Diaz, J. and Joly, P.. A time-domain analysis of PML models in acoustics. Computer Meth. Appl. Mech. Engrg., 195:3820–3853, 2006.Google Scholar
[8]Giles, M.. Nonreflecting boundary conditions for Euler equation calculations. AIAA J., 28:2050–2058, 1990.CrossRefGoogle Scholar
[9]Hagstrom, T.. A new construction of perfectly matched layers for hyperbolic systems with applications to the linearized Euler equations. In Cohen, G., Heikkola, E., Joly, P., and Neittaanmäki, P., editors, Mathematical and Numerical Aspects of Wave Propagation Phenomena, pages 125–129. Springer, 2003.Google Scholar
[10]Hagstrom, T. and Goodrich, J.. Accurate radiation boundary conditions for the linearized Euler equations in Cartesian domains. SIAM J. Sci. Comput., 24:770–795, 2002.CrossRefGoogle Scholar
[11]Hagstrom, T. and Hagstrom, G.. Grid stabilization of high-order one-sided differencing I: First order hyperbolic systems. J. Comput. Phys., 223:316–340, 2007.Google Scholar
[12]Hagstrom, T. and Hagstrom, G.. Grid stabilization of high-order one-sided differencing II: Second order wave equations. Submitted, 2009.Google Scholar
[13]Hagstrom, T., Hariharan, S.I., and Thompson, D.. High-order radiation boundary conditions the convective wave equation in exterior domains. SIAM J. Sci. Comput., 25:1088–1101, 2003.Google Scholar
[14]Hagstrom, T. and Warburton, T.. Complete radiation boundary conditions: Minimizing the long time error growth of local methods. SIAM J. Numer. Anal., 47:3678–3704, 2009.CrossRefGoogle Scholar
[15]Hu, F.. A stable, perfectly matched layer for linearized Euler equations in unsplit physical variables. J. Comput. Phys., 173:455–480, 2001.CrossRefGoogle Scholar
[16]Rudy, D. and Strikwerda, J.. A nonreflecting outflow boundary condition for subsonic Navier-Stokes calculations. J. Comput. Phys., pages 55–70, 1980.Google Scholar