Volume 55, 2021Regular articles published in advance of the transition of the journal to Subscribe to Open (S2O). Free supplement sponsored by the Fonds National pour la Science Ouverte
|Page(s)||S535 - S571|
|Published online||26 February 2021|
Discrete transparent boundary conditions for the two-dimensional leap-frog scheme: approximation and fast implementation
Institut de Mathématiques de Toulouse, UMR5219, Université de Toulouse, CNRS, Université Paul Sabatier, F-31062 Toulouse Cedex 9, France.
2 Institut de Mathématiques de Toulouse, UMR5219, Université de Toulouse, CNRS, INSA, F-31077 Toulouse, France.
* Corresponding author: firstname.lastname@example.org
Accepted: 25 July 2020
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.
Mathematics Subject Classification: 65M06 / 65M12
Key words: Transport equation / leap-frog schemes / transparent boundary conditions / stability
© The authors. Published by EDP Sciences, SMAI 2021
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