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Discrete transparent boundary conditions for the two-dimensional leap-frog scheme: approximation and fast implementation
- 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.
- Subjects :
- Coupling
Numerical Analysis
Applied Mathematics
010102 general mathematics
Mathematical analysis
Finite difference
leap-frog schemes
stability
01 natural sciences
Domain (mathematical analysis)
Regular grid
010101 applied mathematics
Computational Mathematics
Transport equation
Normal mode
Modeling and Simulation
Rectangle
Boundary value problem
0101 mathematics
[MATH]Mathematics [math]
Convection–diffusion equation
transparent boundary conditions
Analysis
Mathematics
Subjects
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⟩