Simulation Steps

Three Stages of The Simulation
1 Stokes Stage
The Navier-Stokes equations, in their complete form, take into account inertial effects and unsteadiness. The exact state of flow at t=0 is not crucial to the final solution, but we still need to start with a reasonable approximation. To achieve it, we begin with a simplified version of the equations, assuming no inertia or time-dependence, and we allow no deformations of the mesh for the first 50 iterations. The resulting flow (see figure above) is simplistic, but a good enough starting point. Notice, for instance, how the water flows fastest (red) and slowest (blue) more or less where you would expect.
2 Navier-Stokes simulation with space-time treatment
Now we may allow surface deformation (see figure) and take inertia and time-dependence into consideration for a much more realistic flow. Instead of four nodes per tetrahedral element, the time-space simulation uses eight, and the number of nodes must be doubled accordingly in the input files. For each time-step, several nonlinear iterations are performed, in the following order: Solve for position of the surface (advection equation) Solve for node displacement (linear elasticity) Solve for flow field (N-S equations) Return to 1.
3 Reduced Stabilization	After 400 time-steps, much of the initial turbulence has subsided and we can reduce the stabilization parameter from 2 to 1 (see next page).