A fully nonlinear Boussinesq model in generalized curvilinear coordinates

Fengyan Shi*, Robert A. Dalrymple, James T. Kirby, Qin Chen, Andrew Kennedy

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

97 Scopus citations

Abstract

Based on the fully nonlinear Boussinesq equations in Cartesian coordinates, the equations in generalized coordinates are derived to adapt computations to irregularly shaped shorelines, such as harbors, bays and tidal inlets, and to make computations more efficient in large near-shore regions. Contravariant components of velocity vectors are employed in the derivation instead of the normal components in curvilinear coordinates or original components in Cartesian coordinates, which greatly simplifies the equations in generalized curvilinear coordinates. A high-order finite difference scheme with staggered grids in the image domain is adopted in the numerical model. The model is applied to five examples involving curvilinear coordinate systems. The results of these cases are in good agreement with analytical results, experimental data, and the results from the uniform grid model, which shows that the model has good accuracy and efficiency in dealing with the computations of nonlinear surface gravity waves in domains with complicated geometries.

Original languageEnglish (US)
Pages (from-to)337-358
Number of pages22
JournalCoastal Engineering
Volume42
Issue number4
DOIs
StatePublished - Apr 2001

Keywords

  • Boussinesq equations
  • Curvilinear coordinates
  • Finite difference method
  • Numerical model

ASJC Scopus subject areas

  • Environmental Engineering
  • Ocean Engineering

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