Choosing a stretching factor in DIVEMesh - wave number
 

High there,

I've been reading through the paper "Reduction of the wave propagation error of a sigma grid based numerical tank using a vertical spacing based on the constant truncation error" by Pakozdi et al. (2021.https://doi.org/10.1016/j.oceaneng.2021.109741) and am trying to work out the way to compute the optimum grid spacing profile so that I can compare this profile with that computed by the grid stretching function in DIVEMesh and estimate the ideal stretching factor for my simulation.

I am confused in the paper what the "wave number" is and how this property is found and used to normalise a number of variables. I am trying to understand after kdz (normalised grid spacing) is computed, it can be converted back to z (not normalised) to compared to the DIVEMesh profile.

I am also not sure what value to set k (wave number) to when trying to numerically solve the equation for kdz.

I hope this makes sense and there is a simple way to wrap my head around this so that I can find the optimum grid spacing.

Cheers,
Felix

Hi Felix,
I am not sure if I understood your question correctly.
Wave number k= 2*pi/L.
In the case of regular waves, this is the wavelength L of the desired input wave.
In the case of irregular waves, 5.4, 5.5 and 5.6 in the paper you mention offers some guidelines for the basis of L for the stretching.

Then, to use your custom stretching in Divemesh, you need to then create a file with one column going 0 to 1 based on the optimal stretching.
This file is to named z-spacing.dat
and the stretching for the z-direction using this file is activated by B 103 10

Hope that helps

Thanks Kamath,

That makes a lot of sense and clear it all up!

Cheers
Felix