Stratified flow over an obstacle: a numerical experiment

Abstract

Numerical studies of time-dependent, two-dimensional, stratified flow of incompressible, viscous, diffusive fluid are described. The particular physical problem which has been considered is that of stratified flow over a vertical fence when the motion is impulsively started from rest. Solutions have been calculated for the following two cases: Re = 397, Pr = 10, Ri = 1.58; and Re = 5000, Pr = 1, Ri = 1.58. The results are presented as contour plots of the flow variables, generated directly by the computer. A new iterative method was used for numerical integration of the governing equations and was found to be very effective. The method is based on the combination of the Crank-Nicolson method with a strongly implicit iterative method developed by Stone (1968). Full details of the method are given together with a summary of its performance on the problems calculated. It is shown that proper treatment of the inflow and outflow boundary conditions is crucial for successful numerical modeling of stratified flows.