SEMI-INFINITE ELEMENTS FOR NON-REFLECTING BOUNDARY CONDITIONS
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Authors
Riggs, Jessica M.
Subjects
non-reflecting boundary conditions
Galerkin methods
semi-infinite elements
scaled Laguerre functions
Galerkin methods
semi-infinite elements
scaled Laguerre functions
Advisors
Giraldo, Francis X.
Kelly, James, Naval Research Laboratory
Date of Issue
2024-06
Date
Publisher
Monterey, CA; Naval Postgraduate School
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Abstract
Models of the ocean and atmosphere require solving systems of partial differential equations with boundary conditions which emulate an infinite domain. The goal of non-reflecting boundary conditions is to eliminate spurious waves that can be reflected back into the model and interfere with the simulation. The issue of reflections is usually solved by dedicating a portion of the domain to a sponge layer, which applies damping to the solution within the sponge. However, sponge layers can be computationally expensive and require extensive tuning to a particular problem. Semi-infinite elements are one way to attenuate reflections while avoiding tuning parameters. In this thesis, we solve the one-dimensional shallow water equations using a continuous Galerkin method based on the Legendre-Gauss-Lobatto points and use the Laguerre-Gauss-Radau points to formulate a semi-infinite element scheme. We compare the results of the Laguerre semi-infinite element formulation to the results from a standard multi-element Lobatto polynomial sponge layer. We found that the Laguerre semi-infinite element formulation attained similar performance to the Lobatto sponge layer in attenuating reflections in the domain. We observed numerical noise in the boundary element of the Laguerre semi-infinite element formulation that may affect the solution in more complex problems.
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Thesis
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Distribution Statement
Distribution Statement A. Approved for public release: Distribution is unlimited.
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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.