Simulation of Mass Transport in Rotating Flow Using the Finite Element Method

Abstract

This paper presents simulation of streamline patterns and mass transport within a rotating (circulating) region of flow approximated by a square on the side of a channel. The steady rotating flow is assumed two-dimensional (depth-averaged) and is generated and maintained by a uniform main flow at the open boundary. The equation governing mixing and transport of a finite quantity of conservative tracer instantaneously introduced at a location in the flow field has been numerically solved. The numerical scheme is based on the finite element approximation of the governing differential equation and uses the method of weighted residuals. The flow field is represented by triangular elements, and linear basis functions are used in the interpolation scheme. The unsteady term in the mass transport equation is approximated by finite differencing in full-forward time steps. The diffusion coefficient has been represented as a tensor, the components of which are functions of diffusion coefficients along and normal to the streamlines.