Three Stages of The Simulation

1Stokes Stage 

The NavierStokes
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 timedependence, 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.

2NavierStokes simulation with spacetime treatment 

Now we may allow surface deformation (see figure) and take inertia and timedependence into
consideration for a much more realistic flow.
Instead of four nodes per tetrahedral element, the timespace simulation uses eight, and the number of nodes must be doubled accordingly in the input files.
For each timestep, 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 (NS equations)
 Return to 1.

3
Reduced Stabilization 
After 400 timesteps, much of the initial turbulence has subsided and we can reduce the stabilization parameter
from 2 to 1 (see next page).
