We have implemented a sophisticated incompressible flow solver using DIME and DIMEFEM. The algorithm is described more completely in [Bristeau:87a]. The evolution equation for an incompressible Newtonian fluid of viscosity n is
We use a three-stage operator-split scheme whereby for each time step of length dt, the equation is integrated
The parameter is .
Each of these three implicit steps involves the solution of either a Stokes problem:
or the nonlinear problem:\
where is a parameter inversely proportional to the time step. We solve the Navier-Stokes equation, and consequently also these subsidiary problems, with given velocity at the boundary (Dirichlet boundary conditions).