Discrete transparent boundary conditions for parabolic equations

• Published in: The Journal of the Acoustical Society of America Vol. 130; no. 4_Supplement; p. 2528
• Main Author: Pannatoni, Ronald F.
• Format: Journal Article
• Language: English
• Published: 01.10.2011
• ISSN: 0001-4966; 1520-8524
• DOI: 10.1121/1.3655094

There are simple algorithms for constructing transparent boundary conditions (TBCs) for a partial discretization of the basic parabolic equation that is known as a “semi-discrete” parabolic equation. This equation and some of these algorithms are reviewed. Solutions of a semi-discrete parabolic equation in a long rectangular strip subject to TBCs at the long edges of the strip are then considered. These solutions can be computed accurately and efficiently with a pseudospectral method that is based on expansions in Chebyshev polynomials. It is beneficial to combine this method with a conventional split-step FFT solution of a parabolic equation subject to Neumann boundary conditions at the long edges of the strip. This hybrid approach will be called the “decomposition method.” It is demonstrated in a computation of radiation modes from the termination of a truncated nonlinear internal gravity wave duct in a shallow water area.