# Pseudospectral procedure for the solution of nonlinear wave equations with examples from free-surface flows

Paul A. Milewski, Esteban G. Tabak

Research output: Contribution to journalArticle

### 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.

Original language English (US) 1102-1114 13 SIAM Journal on Scientific Computing 21 3 Published - Nov 1999

### Fingerprint

Free Surface Flow
Nonlinear Wave Equation
Wave equations
Wave Operator
Integrating Factor
Stratified Flow
Rotating Flow
Wave Interaction
Forcing Term
Surface Waves
Topography
Solitary Waves
Wave Propagation
Diffraction
Stiffness
Factorization
Eliminate
Three-dimensional
Solitons
Surface waves

### ASJC Scopus subject areas

• Mathematics(all)
• Applied Mathematics

### Cite this

In: SIAM Journal on Scientific Computing, Vol. 21, No. 3, 11.1999, p. 1102-1114.

Research output: Contribution to journalArticle

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