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Projection-Method with grid generated via Thompson algorithm (stretching function)

Hi all,

I'm trying to implement the projection method on a flow past a cylinder problem.

I have generated a grid for the cylinder via Thompson algorithm of the Poisson equations. Therefore the grid is (very) stretched and curvilinear.

When I descretize the NS equations, what is the appropriate stretching function I should use?

For example, for $x=x(\xi,\eta)$
$\frac{du}{dx} = \frac{du}{d\eta}\frac{d\eta}{dx}+ \frac{du}{d\xi}\frac{d\xi}{dx}$

what is the appropriate expression for $\frac{d\eta}{dx},\frac{d\xi}{dx}$ ?