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tamer June 12, 2003 02:46

Non linear coupled boundaies
 
In recent posting I read. Re: Time Step Restriction

Posted By: Jason Wei <nwei600@netscape.net> Date: Mon, 5 May 2003, 10:06 a.m.

In Response To: Time Step Restriction (Valdemir)

Actually there are no theoratical formulas to determine the time step restriction for the nonlinear differential equations. They are only available for linear PDEs. The rule of thumeb is to make the discretization as implicit as possible. Don't just throw all the nonlinear terms in the source term, you can linearize it and put the higher order truncation terms in the source term. The other qualitative rule is to reduce the time step whenever you reduce the spatial grid size, especially in the dominant flow direction. ____________________ I totaly agree about the message content but I wonder if the problem turn to be a slow convergance and need to small time steps just because of non-linear boundary conditions that involve multivariable. Is there is a way to easly overcome the problem and linearize the b.c? The problem I tackle involve solving the continuity and both momentum equation (x &y)and the concenrtation (C) equation. Where in the concentration b.c, we have: D dC/dy = V C D is diffusion coeff, C is the concentratio, V is the Y-velocity. V at the boundary is given by: V=(P-pi)/R/mu, P is the presure and R, mu are constants. pi = f(C) cubic function.

So, the boundary is really complex funcation, any suggestion how linearize it to make it as implicit as possible?


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