[Hillie]

Hi all,

I was faced with the following problem: I have a nice unstructured mesh 2D mesh in GMSH, and I want to extrude this mesh with a certain growth ratio to a 3D mesh. The extrude command in GMSH lets you easily make an extrusion were all the layers are the same height, but making the layer vary in size was the problem.

I have spend most of my afternoon on the problem size I couldn't find any good solution online, and to make sure other don't have to I though I would share the solution I came up with.

A standard Extrusion will go like this:

surfaceVector[] = Extrude{0, 0, thickness}
        {
        Surface{surfacenumber}  ;
        Layer{number of layers};
        Recombine;
       }

With the Layers command you can vary this size of the layers in the following way:

Layers{{number of cells per layer}, {relative thickness of the layer}}

What I have done is to to create an x amount of 1 cell layers , where x is the amount of cells that you want in the extrusion. To do this I have created a little python script.

@author: hilbert
"""

import numpy as np

initial_mesh_height=1*10**-5  #initial mesh height

blh=0.004                 #required height
n=4.0;                   #amount of cells


#solve for the growth ratio r
rtry=np.linspace(0.5, 1.5, 1000)
error=(1-np.power(rtry,(n)))/(1-rtry)-blh/initial_mesh_height
r=rtry[np.argmin(np.abs(error))]

rtry=np.linspace(r-0.1, r+0.1, 1000000)
error=(1-np.power(rtry,(n)))/(1-rtry)-blh/initial_mesh_height
r=rtry[np.argmin(np.abs(error))]


blh=initial_mesh_height*(1-r**n)/(1-r)   #compute the extrusion height and see if it matches, i.e how good was our solution for r
#print blh

hts=[]   #the place to put cells
layer=[] #a placeholder for the amount of cells per layer , i.e 1
ht=0     #initialize layer height
for i in range(int(n)):
    h=initial_mesh_height*r**i
    ht+=h
    hts.append(ht/blh)
    layer.append(1)
    #print ht/blh

#print hts
#print layer

This is for a simple geometric expansion, i.e the initial cell grows with a growth ratio r each layer. In the script you pop in the initial cell height, the extrusion height and the amount of cells that you want.

the script then computes the growth ratio. Then pop the relative heights hts in the layer command.

As an example with the inputs as given it gives
layer=[1, 1, 1, 1]
hts=[0.10803802938634398, 0.28089887640449435, 0.55747623163353499, 1.0]

In you then give:
Layers{{1, 1, 1, 1}, {0.10803802938634398, 0.28089887640449435, 0.55747623163353499, 1.0}}

Hope it helps ,
Cheers

[chomikzimon]

Hi!

Thank you for your post. It is very helpful. Could you let me know if it is possible to have the boundary layers with extrusion but decreasing in height? Simply reversing the layer height in Gmsh does not seem to work.

Thank you for your time!

[Hillie]

He,

With the extrude command you can't since the heights needs to be increasing:
, see http://gmsh.info/doc/texinfo/gmsh.html#index-extrude, section 6.3.2

Can't you use a symmetry condition to avoid having to simulate a full boundary layer?