Hi,

I have a transient simulation where I expect the solution never to reach a steady state (perhaps a periodic steady state though). However this is not the case (it reaches steady state quite rapidly). How come? I have a few suggestions, can you please tell me what you think?

1. Using an implicit method I might have too high time step at some points in the simulation, thus violating the CFL condition, and hence not describing the transient behaviour adequately.

2. Using an implicit method of 1st order the resolution in time might not be enough (coupled to nr 1 above).

3. The simulated system is symmetrical, but the physical system might be - not fully symmetrical.

Best Regards

Sara

Dear Sara,

My suggestions are as follows

1. Implicit methods cannot be used in the framework of transient solvers as you do it for a steady state framework. You can definitely use it in a dual time framework, violate CFL condition and update your variables, though.

2. First order implicit scheme are not generally preferred fot time -accurate simulations. Temporal accuracy of 2 (BDF/Crank-Nicholson) is usually favoured.

3. The response of the system you attempt to simulate is closely tied to the physics. If you have a symetrically oscillating airfoil, you attempt to numerically simulate the response of this oscillation, which expectedly must mimick the symmetry of oscillation.

If you are trying to use an implicit scheme the way you use it on a steady state solver and simulate a transient problem, you would possibly end up in steady state and quite quickly. If you are using a steady state solver and want to simulate an unsteady phenomenon, with least change to your code, I suggest that you use a first order explicit time stepping with CFL criterion to see the "periodic behaviour", though it could take quite a lot of iterations before you actually achieve the transient response.

Regards,

Ganesh

Inadequate spatial resolution or a low-order approximation for the spatial gradients can sometimes lead to numerical damping. Also use of upwinding for advective terms must be carefully considered.