I have an obviously simple question. When one uses a finite-volume method (Peric) and does steady flow over a sphere at a Reynolds number of 100 a converged solution is obtained as the flow is steady axisymmetric for this Reynolds number.When one repeats the same calculations with unsteady equations and with a large time step (~1) a converged solution (i.e. minimum Residual reached) is obtained in few time steps. When the time-step is decreased (~10^-4), the residuals are very large and one gets unphysical solutions. For above the equations are non-dimensionalised by setting density=100 and viscosity=1.

1. My question is that if the flow is basically steady the unsteady terms should be zero and the flow should converge even for a transient simulation. Why does it converge for a transient simulation only if the time-step is large ?

2. Also the outflow boundary has to be placed at a large distance downstream for low Reynolds number flows as compared to high Reynolds number cases all other things remaining same. Why ?

I would appreciate if somebody bothered about the same problems and shares his experience with me.

Thanks is Advance.

Raaj.

1. It is quite strange that your unsteady calculation converges with large Dt in several time steps, but not converge with small Dt. This requires check of your code validation; 2. For low Re number, it is more close to Stokes flow, the elliptic nature makes the attenuation of disturbance slower with distance from the body in all directions. Therefore the upstream BC should be the same away with that of downstraem BC. It is above 5 diameters I think.

As our experience and proved by numerical consideratin that lower Dt increase the accuracy to the real results and higher Dt decrease it. The lower Dt should to easy to converge and get real results. I think there is something wrong in your computer code

You both want to say that if you compute a steady-flow with unsteady equations and a very small time step, the results should converge (and be better than using steady equations) !

Raaj.

This has something to do with the artificial dissipation (or potentially in your upwind scheme) in your code. Large time step increses the artificial dissipation effect. For unsteady problem, use higher order scheme, both in space and time. Also use small real time step to ensure the CFL is not too big on most of the cells. It will give your trouble if it is much larger than one. I calculated an unsteady supersonic flow. The results are sensitive to these parameters.

Regards,

Guoping

Exactly...CFL is very important here. high CFL may b leading to unstability.

Is the CFL number important for a fully implicit scheme? I am using a sofi scheme.