[G. matton]

hello,

I want to transform a code( Rans-2DV-WENO-SIMPLIC- sigma Coordinate) into a vertical streched version to statifity the y+ condition in deep waters. The original code use a uniform mesh in the vertical, the vertical grid number is 8000 to meet y+=100 in my simulation, which is too expensive. Therefore, I should apply the vertical stretched version.

But I have no idea how to use the exponentially stretched grid. Could some one be so nice to tell me how to deal with it? Is there any example to study?

I think there should be a transform function, so the compution domain is uniform, and the scheme used in the original code still works.

thanks in advance

[FMDenaro]

Why do you want to compute the discrete derivatives in the computational plane? Use the formula for non uniform grid.

[G. matton]

Hello FMDenaro, the original code apply a geometric multigrid with red-black SOR method to solve possion function, and the advection is sloved by the WENO scheme. In the computational plane（uniform grid）these scheme may work. This is why i want to do calculations in the computational plane. Very thanks to you.

[FMDenaro]

Originally Posted by G. matton

Hello FMDenaro, the original code apply a geometric multigrid with red-black SOR method to solve possion function, and the advection is sloved by the WENO scheme. In the computational plane（uniform grid）these scheme may work. This is why i want to do calculations in the computational plane. Very thanks to you.

The transformation you asked is described in sec 3.1 Here
https://www.researchgate.net/publica...-uniform_grids

But you need to transform the equations from the physical to the computational plane. This is a topic you can find in the classic textbooks about structured grid generations.

[G. matton]

Thanks very much, FMDenaro.
I hope tp do the exponentially stretched grid in the sigma coordinate. In the physical domain, the bottom is the sea bed and the up is the free-surface. In the computational domain 1 (for the original code), the bottom is 0 and the up is 1. This transformation is clear and many model does this. However, when I want to use stretched grid in the computational domain 1, and by some transformation like sigma-transformation, the stretched grid will be uniform in the computational domain 2 (for the stretched code version), and the scheme used in the original code can be easily applied into the stretched one.

[FMDenaro]

Originally Posted by G. matton

Thanks very much, FMDenaro.
I hope tp do the exponentially stretched grid in the sigma coordinate. In the physical domain, the bottom is the sea bed and the up is the free-surface. In the computational domain 1 (for the original code), the bottom is 0 and the up is 1. This transformation is clear and many model does this. However, when I want to use stretched grid in the computational domain 1, and by some transformation like sigma-transformation, the stretched grid will be uniform in the computational domain 2 (for the stretched code version), and the scheme used in the original code can be easily applied into the stretched one.

yes, but there is the fact you need the metric, that is the Jacobian for the derivatives.

[G. matton]

Thanks very much.I will learn from your suggestion