Abstract
A numerical procedure for solving the time-dependent, incompressible Navier-Stokes Equations and the heat and salinity transport equations, coupled through the density-state equation, is presented. The method is based on a set of finite element equations formulation and timemarching procedure. The finite element formulations consist of two steps, i.e. a first step for the vertical distributions of the primitive variables of interest through the depth using Chebyshev polynomials and a second step for the horizontal distributions of the coefficients of the polynomials using a two-dimensional triangular basis set. And the time-marching procedure is executed with the Kawachi and FT explicit schemes combined with the velocity correction technique. The fully three-dimensional reproduction of the convective currents and salinity and heat transports is accomplished with the aid of Petrov Galerkin integrations with the well-defined triangular basis set in the horizontal domain. As a demonstrative model operation, vertical circulations with caballing effect and inverse gravitational circulations with topographic heat accumulation effect are analyzed in hypothetical water bodies. The computed results have shown quite good agreement with the expected ones. Consequently the model is proved to be a useful tool in analyses of density driven flows.
