hi, I am using fractional step method to simulate flow over square cylinder. The initial condition we impose should be divergent free in fractional step method. But if I give inlet velocity as 1 and velocity at other points be zero, it will not be divergent free, so the method is not converging. please help me how to impose initial condition if we generate external flows using fractional step method..

Its better if you impose the same free-stream conditions on velocity for the entire grid. (u=const, v=const). It will also be good if you can supply the initial pressure based on u=const, v=const (by solving a pressure poisson equation initially). -Dominic

dear dominic,

Thank you very much for your helpful suggestion. I have one more issue to be sorted out before making my code a reliable one. I am using Adams Bashforth Scheme for convective terms, which appriximates it using nth and (n-1)th values. So I need two guesses n and (n-1) velocity values. Is it good to take both values as you mentioned or does it need special approximation? Thanks in advance

> The initial condition we impose should be divergent free in fractional step
: method. But if I give inlet velocity as 1 and velocity at other points be zero,
: it will not be divergent free, so the method is not converging.

Not usually. If a scheme does not act to drive out the mass errors present at time level n then after many time steps the small residual mass errors after each time step will almost certainly start to accumulate and cause a numerical instability.

I think your problem may lie elsewhere. What scheme are you following?

> please help me how to impose initial condition if we generate external
: flows using fractional step method.

For a normal scheme it should not matter in terms of stability but the first few time steps with large global mass errors are obviously not physically correct solutions.

Alternatively, if you solve your Poisson equation down to a tight tolerance many schemes will give a mass conserving flowfield after the first time step even with non-mass conserving initial conditions.

hi andy, thank you very much for your reply. I am following the paper "The Fractional-Step Method for the Navierâ€"Stokes Equations on Staggered Grids: The Accuracy of Three Variations" by armfield and street JCP, 1999. From that paper I am using the non-iterative scheme. Will it work even if I give non-divergent free initial velocity conditions? I am using line SOR to solve pressure poisson equation. Will it be a problem?