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.
Accepté le :
Publié le :
DOI : 10.1051/m2an/2020052
Keywords: Transport equation, leap-frog schemes, transparent boundary conditions, stability
@article{M2AN_2021__55_S1_S535_0,
author = {Besse, Christophe and Coulombel, Jean-Fran\c{c}ois and Noble, Pascal},
title = {Discrete transparent boundary conditions for the two-dimensional leap-frog scheme: approximation and fast implementation},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {S535--S571},
year = {2021},
publisher = {EDP-Sciences},
volume = {55},
number = {Suppl\'ement},
doi = {10.1051/m2an/2020052},
zbl = {1481.65122},
mrnumber = {4221310},
language = {en},
url = {https://www.numdam.org/articles/10.1051/m2an/2020052/}
}
TY - JOUR AU - Besse, Christophe AU - Coulombel, Jean-François AU - Noble, Pascal TI - Discrete transparent boundary conditions for the two-dimensional leap-frog scheme: approximation and fast implementation JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2021 SP - S535 EP - S571 VL - 55 IS - Supplément PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/m2an/2020052/ DO - 10.1051/m2an/2020052 LA - en ID - M2AN_2021__55_S1_S535_0 ER -
%0 Journal Article %A Besse, Christophe %A Coulombel, Jean-François %A Noble, Pascal %T Discrete transparent boundary conditions for the two-dimensional leap-frog scheme: approximation and fast implementation %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2021 %P S535-S571 %V 55 %N Supplément %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/m2an/2020052/ %R 10.1051/m2an/2020052 %G en %F M2AN_2021__55_S1_S535_0
Besse, Christophe; Coulombel, Jean-François; Noble, Pascal. Discrete transparent boundary conditions for the two-dimensional leap-frog scheme: approximation and fast implementation. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 55 (2021), pp. S535-S571. doi: 10.1051/m2an/2020052
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