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hedge November 27, 2007 10:24

convergence in unstedy problems

I'm trying to solve an unsteady problem with moving shocks in fluent. I'm using density based solver, second order upwind discretization and Roe flux difference splittiong.

I would like to check the convergence of the solution in the following way. I get a several grids (with cell sizes h of 1e-5 m, 5e-6 m 2.5e-6 m and so on). I get the strict location in the space, say x*=3e-3 m and specific time moment, say t*=2.8e-6 sec, after the shock wave passed this point. Another point was x**=-1.2e-3 m, where no shocks and only rarefactions are present.

For all the grids I made the runs and plotted the pressure as function of computational cell size at this time moment at this point.

I guess, that the dependence of the pressure on cell size should be as P(t*,x*) = A + B*h^2 (h - cell size, where the last term is relatively small), i.e. quadratic fuction parabola as I use the second order method.

But I don't. I actually has the linear dependence P(t*,x*) = a + b*h with a very good accuracy, beginning from cell size of 5e-6 m and less. So it means, that I probably have reached the convergence, but with the first order instead of second ones. For the case with the rarefection wave I got the same result.

Could anybody advise me in the follwoing quastions 1) Is this procedure strict for unsteady solvers? 2) does I actually reached the convergence? 2) Does it work in Fluent, when the shock waves are simulated? 3) Does this approach to convergence test applicable to commercial solvers? ;-)

Thanks in advance

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