NUMERICAL-SOLUTION OF UNSTEADY VISCOUS FLOWS

A number of different model transient flow problems are solved using a finite element algorithm. This algorithm is benchmarked against analytical solutions for both pure diffusion and convection-diffusion problems in two dimensions, and the relative merits of algorithmic variations are discussed. This study constitutes the early phase of a broader effort to consider the incompressible Navier-Stokes equations and furthermore the equations for viscoelastic flow. First, consideration is given to transient Couette flows both with an impulsively initiated plate and an oscillating plate. Then, with convection present, linear and nonlinear convection-diffusion problems are addressed.