### 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) |
---|---|

Pages (from-to) | 1102-1114 |

Number of pages | 13 |

Journal | SIAM Journal on Scientific Computing |

Volume | 21 |

Issue number | 3 |

State | Published - Nov 1999 |

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### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*SIAM Journal on Scientific Computing*,

*21*(3), 1102-1114.

**Pseudospectral procedure for the solution of nonlinear wave equations with examples from free-surface flows.** / Milewski, Paul A.; Tabak, Esteban G.

Research output: Contribution to journal › Article

*SIAM Journal on Scientific Computing*, vol. 21, no. 3, pp. 1102-1114.

}

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 - 1999/11

Y1 - 1999/11

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.

UR - http://www.scopus.com/inward/record.url?scp=0033295424&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0033295424&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0033295424

VL - 21

SP - 1102

EP - 1114

JO - SIAM Journal of Scientific Computing

JF - SIAM Journal of Scientific Computing

SN - 1064-8275

IS - 3

ER -