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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Published in | Journal of waterway, port, coastal, and ocean engineering Vol. 131; no. 5; pp. 226 - 238 |
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Main Author | |
Format | Journal Article |
Language | English |
Published |
Reston, VA
American Society of Civil Engineers
01.09.2005
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Subjects | |
Online Access | Get full text |
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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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Bibliography: | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 23 ObjectType-Article-2 ObjectType-Feature-1 |
ISSN: | 0733-950X 1943-5460 |
DOI: | 10.1061/(ASCE)0733-950X(2005)131:5(226) |