Efficient Absorbing Boundary Conditions for Modeling Wave Propagation in Unbounded Domains.

Absorbing boundary conditions;Perfectly Matched L;Semi explicit method

Zahid, Md. Anwar ; Dr. Murthy N Guddati, Committee Chair,Dr. C. C. David Tung, Committee Member,Dr. M. Shamimur Rahman, Committee Member,Dr. Mansoor Haider, Committee Member,Zahid, Md. Anwar ; Dr. Murthy N Guddati ; Committee Chair ; Dr. C. C. David Tung ; Committee Member ; Dr. M. Shamimur Rahman ; Committee Member ; Dr. Mansoor Haider\t ; Committee Member

University:North Carolina State University

关键词: Absorbing boundary conditions;    Perfectly Matched L;    Semi explicit method;   

Others  :  https://repository.lib.ncsu.edu/bitstream/handle/1840.16/3875/etd.pdf?sequence=1&isAllowed=y

美国|英语

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【 摘 要 】

Many engineering problems (e.g. soil-structure interaction, medical imaging and nondestructive evaluation) encounter the phenomena of wave propagation. Among these problems some involve domains of infinite extent. Standard numerical methods such as finite element and finite difference methods cannot handle the unbounded domain as they are designed for the analysis of bounded domains. In order to solve an unbounded-domain problem, the domain is truncated around a region of interest, and absorbing boundary conditions (ABCs) are applied on the truncation boundary. These ABCs are expected to absorb outgoing waves and mimic the effect of the truncated exterior. Continued-fraction absorbing boundary conditions (CFABCs) are a class of highly efficient ABCs for modeling acoustic wave absorption into unbounded domains. The current versions of CFABCs are applicable only to non-dispersive scalar wave equation and are not effective for dispersive or elastic wave propagation problems. This dissertation contains extensions of CFABCs to dispersive and elastic wave propagation problems. The main difficulty in the case of dispersive wave propagation is that evanescent waves have significant presence and are not treated accurately by original CFABCs. In the first part of the dissertation, CFABCs are modified to effectively absorb propagating as well as evanescent waves.This is achieved with the help of special padding elements that absorb the evanescent waves and standard CFABC elements that are effective in absorbing propagating waves. Called the "padded CFABC", this combination is shown to be a highly efficient and accurate ABC for dispersive wave equations. Numerical results are presented to illustrate the effectiveness of these ABCs. The second part of the dissertation involves the extension of CFABCs to elastic wave propagation problems. Elastic wave propagation is inherently complex because of the strong coupling of pressure and shear waves that propagate at different speeds. It turns out that straightforward extension of acoustic CFABC tends to be unstable for elastic wave propagation problems. Modifying the CFABC by altering the parameters to complex numbers appears to rectify the stability problem. This stabilized CFABC, named "complex CFABC", is not as efficient as the original CFABC, but is superior to existing ABCs for elastic media. The complex CFABC necessitates modification of the implementation including careful operator splitting to achieve efficient explicit computational procedure. These modifications result in an effective and stable complex CFABC for elastic wave propagation, which is illustrated with the help of numerical examples.The ABCs developed in this dissertation are expected to aid in increasing the simulation efficiency for various unbounded domain problems, thus have impact on various fields including earthquake engineering, seismology, soil-structure interaction and shallow water problems.