A pseudospectral procedure for the solution of nonlinear wave equations with examples from free-surface flows

An algorithm for the solution of general isotropic nonlinear wave equations is presented. The algorithm is based on a symmetric factorization of the l inear part of the wave operator, followed by its exact integration through an integrating factor in spectral space. The remaining nonlinear and forcin g terms can be handled with any standard pseudospectral procedure. Solving the linear part of the wave operator exactly effectively eliminates the sti ffness of the original problem, characterized by a wide range of temporal s cales. The algorithm is tested and applied to several problems of three-dim ensional long surface waves: solitary wave propagation, interaction, diffra ction, and the generation of waves by flow over slowly varying bottom topog raphy. Other potential applications include waves in rotating and stratifie d flows and wave interaction with more pronounced topographic features.