Godunov-Based Model for Nonhydrostatic Wave Dynamics
Publication: Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 131, Issue 5
Abstract
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 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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Information
Published In
Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 131 • Issue 5 • September 2005
Pages: 226 - 238
Copyright
© 2005 ASCE.
History
Received: Sep 29, 2003
Accepted: Feb 17, 2005
Published online: Sep 1, 2005
Published in print: Sep 2005
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