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Old   October 12, 2004, 10:39
Default CFL condition
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In the Anderson's Book of CFD, there is a CFL condition for the problem of supersonic flow over a flat plate. There, he use MacCormack explicit in a time-dependent approach.

My problem is I've got a coordinate transformation, x=x(xi,eta), y=y(xi,eta), so that I don't know what to write instead of \Delta x and \Delta y in the CFL condition.

Thanks in advance.
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Old   October 13, 2004, 08:47
Default Re: CFL condition
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Many papers have answers. Let \xi_X and \xi_Y be metrics of corrd. transformation, in a illustrative way, D t= CFL /( |u * \xi_X +v * \xi_Y| + C * sqrt( xi_X**2 +xi_Y**2)). where C is sound speed. Note that the dimenson is consistent with definition of CFL number. One can similarly get Dt from another direction \eta. The minimum of the two is what desired.
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Old   October 13, 2004, 15:38
Default Re: CFL condition
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Thanks versi, very useful! I will try that.

I've got another question. If

x=x(nxi,neta); y=y(nxi,neta);

XI=XI(nxi,neta); ETA=ETA(nxi,neta);

Could you confirm that the next sentence is calcutating the metrics?

XI_x=zeros(nxi,neta); ETA_x=zeros(nxi,neta); XI_y=zeros(nxi,neta); ETA_y=zeros(nxi,neta); for i=2:nxi-1;

for j=2:neta-1;





end end

Thanks if you try that.
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