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Discrete transparent boundary conditions for the two-dimensional leap-frog scheme: approximation and fast implementation

Authors :
Christophe Besse
Jean-François Coulombel
Pascal Noble
Institut de Mathématiques de Toulouse UMR5219 (IMT)
Université Toulouse Capitole (UT Capitole)
Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse)
Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J)
Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3)
Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)
Institut National des Sciences Appliquées - Toulouse (INSA Toulouse)
Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)
ANR-17-CE40-0025,Nabuco,Frontières numériques et couplages(2017)
Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1)
Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3)
Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)
Institut National des Sciences Appliquées (INSA)
Source :
ESAIM: Mathematical Modelling and Numerical Analysis, ESAIM: Mathematical Modelling and Numerical Analysis, 2021, 55, pp.S535-S571. ⟨10.1051/m2an/2020052⟩, ESAIM: Mathematical Modelling and Numerical Analysis, EDP Sciences, 2021, 55, pp.S535-S571. ⟨10.1051/m2an/2020052⟩
Publication Year :
2021
Publisher :
HAL CCSD, 2021.

Abstract

International audience; We develop a general strategy in order to implement approximate discrete transparent boundary conditions for finite difference approximations of the two-dimensional transport equation. The computational domain is a rectangle equipped with a Cartesian grid. For the two-dimensional leap-frog scheme, we explain why our strategy provides with explicit numerical boundary conditions on the four sides of the rectangle and why it does not require prescribing any condition at the four corners of the computational domain. The stability of the numerical boundary condition on each side of the rectangle is analyzed by means of the so-called normal mode analysis. Numerical investigations for the full problem on the rectangle show that strong instabilities may occur when coupling stable strategies on each side of the rectangle. Other coupling strategies yield promising results.

Details

Language :
English
ISSN :
0764583X and 12903841
Database :
OpenAIRE
Journal :
ESAIM: Mathematical Modelling and Numerical Analysis, ESAIM: Mathematical Modelling and Numerical Analysis, 2021, 55, pp.S535-S571. ⟨10.1051/m2an/2020052⟩, ESAIM: Mathematical Modelling and Numerical Analysis, EDP Sciences, 2021, 55, pp.S535-S571. ⟨10.1051/m2an/2020052⟩
Accession number :
edsair.doi.dedup.....1bad6bd77d178189bf3947d7b698d2ba
Full Text :
https://doi.org/10.1051/m2an/2020052⟩