SWASH: An operational public domain code for simulating wave fields and rapidly varied flows in coastal waters

Shock-capturing non-hydrostatic model for fully dispersive surface wave processes

Non-hydrostatic multi-layer models have become a popular tool in describing wave transformation from deep water to the surf zone, but the numerical approach lacks a theoretical framework to guide implementation and assist interpretation of the results. In this paper, we formulate a non-hydrostatic model in an analytical form for the derivation and examination of dispersive and nonlinear properties. Depth integration of the dimensionless continuity and Euler equations over each layer yields the conventional multi-layer formulation. A variable transformation converts the conventional form into an integrated series form, which provides separate descriptions of flux- and dispersion-dominated processes. Substitution of the non-hydrostatic pressure and vertical velocity in the governing equations by high-order derivatives of the horizontal velocity and surface elevation provides a direct comparison with the Boussinesq equations published in the literature. Implementation of a perturbation expansion extracts the first- and second-order governing equations with respect to the nonlinear parameter. Based on that, we derive analytical solutions of the linear dispersion and the second-order super- and sub-harmonics for up to three layers and optimize the solutions in terms of the layer arrangement. In relation to the Boussinesq equations at comparable orders of expansion, the two- and three-layer models provide slightly higher errors in shallow and intermediate water in terms of dispersion and super-harmonics, but show superior performance in describing sub-harmonics in deep water.

Dispersion and nonlinearity of multi-layer non-hydrostatic free-surface flow

A multi-layer non-hydrostatic model for wave breaking and run-up

A new method for sloshing simulation in a sway tank is present, in which the two phase interface is treated as a physical discontinuity, which can be captured by a well-designed high order scheme. Based on Normalized Variable Diagram (NVD), a high order discretization scheme with unstructured grids is realized, together with a numerical method for free surface flow with a fixed grid. This method is implemented in an in-house code General Transport Equation Analyzer (GTEA) which is an unstructured grids finite volume solver. The present method is first validated by available analytical solutions. A simulation for a 2-D rectangular tank at different excitation frequencies of the sway is carried out. A comparison with experimental data in literature and results obtained by commercial software CFX shows that the sloshing load on the monitor points agrees well with the experimental data, with the same grids, and the present method gives better results on the secondary peak. It is shown that the present method can simulate the free surface overturning and breakup phenomena.

Numerical simulation of sloshing in rectangular tank with VOF based on unstructured grids

A new fully non-hydrostatic model is presented by simulating three-dimensional free surface flow on a vertical boundary-fitted coordinate system. A projection method, known as pressure correction technique, is employed to solve the incompressible Euler equations. A new grid arrangement is proposed under a horizontal Cartesian grid framework and vertical boundary-fitted coordinate system. The resulting model is relatively simple. Moreover, the discretized Poisson equation for pressure correction is symmetric and positive definite, and thus it can be solved effectively by the preconditioned conjugate gradient method. Several test cases of surface wave motion are used to demonstrate the capabilities and numerical stability of the model. Comparisons between numerical results and analytical or experimental data are presented. It is shown that the proposed model could accurately and effectively resolve the motion of short waves with only two layers, where wave shoaling, nonlinearity, dispersion, refraction, and diffraction phenomena occur. Copyright © 2010 John Wiley & Sons, Ltd.

A new fully non‐hydrostatic 3D free surface flow model for water wave motions

Non-hydrostatic finite volume model for non-linear waves interacting with structures

A three-dimensional hydrodynamic and salinity transport model of estuarine circulation with an application to a macrotidal estuary

The three-dimensional Navier-Stokes equations were solved with the fractional step method where the hydrostatic pressure component was determined first, while the non-hydrostatic component of the pressure was computed from the pressure Poisson equation in which the coefficient matrix is positive definite and symmetric. The eddy viscosity was calculated from the efficient k-ɛ turbulence model. The resulting model is computationally efficient and unrestricted to the CFL condition. Computations with and without hydrostatic approximation were compared for the same cases to test the validity of the conventional hydrostatic pressure assumption. The model was verified against analytical solutions and experimental data, with excellent agreement.

Congfang Ai

Papers

A new fully non‐hydrostatic 3D free surface flow model for water wave motions

Non-hydrostatic finite volume model for non-linear waves interacting with structures

A three-dimensional hydrodynamic and salinity transport model of estuarine circulation with an application to a macrotidal estuary

Three-Dimensional Non-Hydrostatic Model for Free-Surface Flows With Unstructured Grid

Numerical investigation of an internal solitary wave interaction with horizontal cylinders