Dear All,

I want to set the initial condition for a lid-driven square cavity flow, which has a u=1 top BC and static BC at other boundaries. I use a Chebychev spectral collocation solver.

Suppose initially the fluid in the cavity is at rest, then there will be serious gradient of u with respect y , which cause the following computation diverge.

Did anyone do similar work? Or could you give any hint?

many thanks in advance

John

are you using the stream-function/vorticity equations to solve this? That is the best way to go about it,in my opinion.

I solved this with a transient technique (algorithm based on the sola half of sola-vof).

At least for low Reynolds numbers (laminar flows), it converges quickly starting with u = v = 0 as an initial condition.

I use the primitive variables for a SPECTRAL (not FVM, FEM ,etc !) collocation solver, say, velocity and pressure. If at t=0, I give a static flowfield as the initial solution except the top boundary (u=1), then the discontinuity in velocity near that boundary will cause an extremely large gradient of du/dy and then ruin the following calculation.

However, this seems not a problem for FVM or FEM.

So I just want ask this question to anyone who has the experience of spectral solver ?

Thanks any way

I've used spectral collocation for this sort of problem. What sort of linear and nonlinear solvers are you using that don't converge? In what way do they not converge? One method is to use continuation in Re (start by solving the linear problem with Re=0) to solve steady N-S (this will fail as you approach transition to turbulence). If you are doing unsteady flow, use the steady solution or the linear Stokes solution as initial condition (you only need a smooth initial condition which is compatible with the boundary conditions).