Application of high-order Higdon non-reflecting boundary conditions to linear shallow water models
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Authors
Neta, Beny
Joolen, Vince van
Dea, John R.
Givoli, Dan
Subjects
non-reflecting boundary conditions
shallow water equation
dispersive wave equation
Higdon boundary conditions
very large domains
shallow water equation
dispersive wave equation
Higdon boundary conditions
very large domains
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Date of Issue
2007
Date
2007
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Abstract
A shallow water model with linear time-dependent dispersive waves in an unbounded domain is considered. The domain is truncated with artificial boundaries B where a sequence of high-order non-reflecting boundary conditions (NRBCs) proposed by Higdon are applied. Methods devised by Givoli and Neta that afford easy implementation of Higdon NRBCs are refined in order to reduce computational expenses. The new refinement makes the computational effort associated with the boundary treatment quadratic rather than exponential (as in the original scheme) with the order. This allows for implementation of NRBCs of higher orders than previously. A numerical example for a semi-infinite channel truncated on one side is presented. Finite difference schemes are used throughout.
A shallow water model with linear time-dependent dispersive waves in an unbounded domain is considered. The domain is truncated with artificial boundaries B where a sequence of high-order non-reflecting boundary conditions (NRBCs) proposed by Higdon are applied. Methods devised by Givoli and Neta that afford easy implementation of Higdon NRBCs are refined in order to reduce computational expenses. The new refinement makes the computational effort associated with the boundary treatment quadratic rather than exponential (as in the original scheme) with the order. This allows for implementation of NRBCs of higher orders than previously. A numerical example for a semi-infinite channel truncated on one side is presented. Finite difference schemes are used throughout.
A shallow water model with linear time-dependent dispersive waves in an unbounded domain is considered. The domain is truncated with artificial boundaries B where a sequence of high-order non-reflecting boundary conditions (NRBCs) proposed by Higdon are applied. Methods devised by Givoli and Neta that afford easy implementation of Higdon NRBCs are refined in order to reduce computational expenses. The new refinement makes the computational effort associated with the boundary treatment quadratic rather than exponential (as in the original scheme) with the order. This allows for implementation of NRBCs of higher orders than previously. A numerical example for a semi-infinite channel truncated on one side is presented. Finite difference schemes are used throughout.
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Communications in Numerical Methods in Engineering, 24, (2008), 1459–1466.
The article of record as published may be located at http://dx.doi.org/10.1002/cnm.1044.
The article of record as published may be located at http://dx.doi.org/10.1002/cnm.1044.
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Applied Mathematics
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This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.