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

- from
**t**to with incompressibility and no convection, then - from to with convection and no incompressibility condition, then
- to
**t + dt**as in stage one with incompressibility and no convection.

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).

Wed Mar 1 10:19:35 EST 1995