TY - JOUR
T1 - Pseudospectral procedure for the solution of nonlinear wave equations with examples from free-surface flows
AU - Milewski, Paul A.
AU - Tabak, Esteban G.
PY - 1999
Y1 - 1999
N2 - An algorithm for the solution of general isotropic nonlinear wave equations is presented. The algorithm is based on a symmetric factorization of the linear part of the wave operator, followed by its exact integration through an integrating factor in spectral space. The remaining nonlinear and forcing terms can be handled with any standard pseudospectral procedure. Solving the linear part of the wave operator exactly effectively eliminates the stiffness of the original problem, characterized by a wide range of temporal scales. The algorithm is tested and applied to several problems of three-dimensional long surface waves: solitary wave propagation, interaction, diffraction, and the generation of waves by flow over slowly varying bottom topography. Other potential applications include waves in rotating and stratified flows and wave interaction with more pronounced topographic features.
AB - An algorithm for the solution of general isotropic nonlinear wave equations is presented. The algorithm is based on a symmetric factorization of the linear part of the wave operator, followed by its exact integration through an integrating factor in spectral space. The remaining nonlinear and forcing terms can be handled with any standard pseudospectral procedure. Solving the linear part of the wave operator exactly effectively eliminates the stiffness of the original problem, characterized by a wide range of temporal scales. The algorithm is tested and applied to several problems of three-dimensional long surface waves: solitary wave propagation, interaction, diffraction, and the generation of waves by flow over slowly varying bottom topography. Other potential applications include waves in rotating and stratified flows and wave interaction with more pronounced topographic features.
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U2 - 10.1137/S1064827597321532
DO - 10.1137/S1064827597321532
M3 - Article
AN - SCOPUS:0033295424
VL - 21
SP - 1102
EP - 1114
JO - Theoretical Computer Science
JF - Theoretical Computer Science
SN - 0304-3975
IS - 3
ER -