A PseudoSpectral Procedure for the Solution of Nonlinear Wave Equations with Examples from Free-Surface Flows

Authors:
Paul A. Milewski;Esteban G. Tabak
Affiliations:
-;-
Venue:
SIAM Journal on Scientific Computing
Year:
1999

Citing 0
Cited 5

Exponential time differencing for stiff systems

Journal of Computational Physics
A composite Runge-Kutta method for the spectral solution of semilinear PDEs

Journal of Computational Physics
Error analysis and applications of the Fourier-Galerkin Runge-Kutta schemes for high-order stiff PDEs

Journal of Computational and Applied Mathematics
L2-stability analysis of novel ETD scheme for Kuramoto-Sivashinsky equations

Journal of Computational and Applied Mathematics
The generation of capillary-gravity solitary waves by a surface pressure forcing

Mathematics and Computers in Simulation

Quantified Score

Hi-index	0.01

Visualization

Abstract

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.