An implicit three-dimensional numerical model to simulate transport processes in coastal water bodies

Abstract

A three‐dimensional baroclinic numerical model has been developed to compute water levels and water particle velocity distributions in coastal waters. The numerical model consists of hydrodynamic, transport and turbulence model components. In the hydrodynamic model component, the Navier–Stokes equations are solved with the hydrostatic pressure distribution assumption and the Boussinesq approximation. The transport model component consists of the pollutant transport model and the water temperature and salinity transport models. In this component, the three‐dimensional convective diffusion equations are solved for each of the three quantities. In the turbulence model, a two‐equation k–ϵ formulation is solved to calculate the kinetic energy of the turbulence and its rate of dissipation, which provides the variable vertical turbulent eddy viscosity. Horizontal eddy viscosities can be simulated by the Smagorinsky algebraic sub grid scale turbulence model. The solution method is a composite finite difference–finite element method. In the horizontal plane, finite difference approximations, and in the vertical plane, finite element shape functions are used. The governing equations are solved implicitly in the Cartesian co‐ordinate system. The horizontal mesh sizes can be variable. To increase the vertical resolution, grid clustering can be applied. In the treatment of coastal land boundaries, the flooding and drying processes can be considered. The developed numerical model predictions are compared with the analytical solutions of the steady wind driven circulatory flow in a closed basin and of the uni‐nodal standing oscillation. Furthermore, model predictions are verified by the experiments performed on the wind driven turbulent flow of an homogeneous fluid and by the hydraulic model studies conducted on the forced flushing of marinas in enclosed seas. Copyright © 2000 John Wiley & Sons, Ltd.

Conjunction of 2D and 3D modified flow solvers for simulating spatio-temporal wind induced hydrodynamics in the Caspian Sea

“…Using an analogy to the speed of sound in the equation of state of compressible flow, the parameter β was introduced (Balas and Zhan 2000;Chorin 1967;Turkel 1986). However, the value of the parameter may be considered as a function of local velocity using the following formula (Dreyer 1990;):…”

“…The momentum equation required a balance between the gravitational force due to the surface elevation gradient, the vertical diffusion of momentum, and the surface wind drag. The formula for constant vertical eddy viscosity is given as (Balas and Zhan 2000):…”

A Composite Finite Element-Finite Difference Model Applied to Turbulence Modelling

“…Developed model is capable of computing water levels and water particle velocity distributions in three principal directions by solving the Navier-Stokes equations. The governing hydrodynamic equations in the three dimensional cartesian coordinate system with the z-axis vertically upwards, are [5], [6], [7], [8]:…”

A Sensitivity Study for the Second Order Reliability-Based Design Model of Rubble Mound Breakwaters

“…The variability is inherent in the derivation of equations in which the scatter in the experimental data is plainly represented by characteristic values (Balas L., 1998). The uncertainty variables (Y i ) introduced into limit-state equations and their statistical properties are summarized in Table 2.…”