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.

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.

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;

XI_x(i,j)=(XI(i+1,j)-XI(i-1,j))/(x(i+1,j)-x(i-1,j));

ETA_x(i,j)=(ETA(i,j+1)-ETA(i,j-1))/(x(i,j+1)-x(i,j-1));

XI_y(i,j)=(XI(i+1,j)-XI(i-1,j))/(y(i+1,j)-y(i-1,j));

ETA_y(i,j)=(ETA(i,j+1)-ETA(i,j-1))/(y(i,j+1)-y(i,j-1));

end end

Thanks if you try that.