Three Stages of The Simulation
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.
2Navier-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.
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).