Finite-element solution of navier-stokes equations for transient two-dimensional incompressible flow

Abstract

A method is described for the solution of transient, incompressible viscous flow in two dimensions. The dependent variables, stream function and vorticity, were approximated over each triangular element using linear interpolation functions. This approximation reduces the problem to a set of matrix equations whose term involving derivatives of time is the mass matrix. The lumping of this matrix together with the application of Euler integration scheme produces an efficient method of solution. Once the nodal values of the stream function are known the velocities and pressure can be computed. As an application a study of the vortex street development behind a rectangular obstruction is described. The flow has been impulsively accelerated to a constant speed in a channel of finite width. The Reynolds number range investigated is between 20 and 100.