Godunov-Based Model for Nonhydrostatic Wave Dynamics

A new numerical model based on the incompressible, nonhydrostatic Navier-Stokes equations for free surface flow is developed. The equations are transformed vertically to the σ coordinate system and laterally to an orthogonal curvilinear system and solved in a fractional step manner in which the pres...

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Bibliographic Details
Published inJournal of waterway, port, coastal, and ocean engineering Vol. 131; no. 5; pp. 226 - 238
Main Author Bradford, Scott F
Format Journal Article
LanguageEnglish
Published Reston, VA American Society of Civil Engineers 01.09.2005
Subjects
Applied sciences
Buildings. Public works
Coastal oceanography, estuaries. Regional oceanography
Earth, ocean, space
Exact sciences and technology
External geophysics
Hydraulic constructions
Physics of the oceans
Port facilities and coastal structures. Lighthouses and beacons
TECHNICAL PAPERS
Solitary wave
Shoals
Shoreline
Stokes wave
Cnoidal wave
Boundary condition
Coastal zone
Hydrostatics
Flow simulation
Wave propagation
Navier Stokes equation
Free surface flow
Numerical simulation
Coastal environment
Numerical models
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Summary:A new numerical model based on the incompressible, nonhydrostatic Navier-Stokes equations for free surface flow is developed. The equations are transformed vertically to the σ coordinate system and laterally to an orthogonal curvilinear system and solved in a fractional step manner in which the pressure is split into hydrostatic and nonhydrostatic components. The model treats the nonhydrostatic term implicitly and uses a collocated grid and pressure interpolation to prevent checkerboard solutions that occur when the velocity and pressure become decoupled. Advection and hydrostatic pressure terms are integrated explicitly with a second-order accurate predictor-corrector scheme. The corrector utilizes fluxes that are computed in a Godunov-based manner by solving a Riemann problem at each cell face. Flow variables are reconstructed at each cell face to obtain second-order spatial accuracy. Numerical simulations of Stokes, cnoidal, and solitary waves with the proposed method and a reference method in which the hydrostatic pressure is implicitly integrated are compared with analytical solutions and experimental data.
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ISSN:0733-950X
1943-5460
DOI:10.1061/(ASCE)0733-950X(2005)131:5(226)