[OpenFoam12]

Hi,

I am trying to understand the double progression (Bump) in gmsh, but I can't wrap my head around it. I have searched on-line and came to the following code;

Point(1) = {0,0,0,1}; 
Point(2) = {1,0,0,1}; 
Point(3) = {3,0,0,1}; 
Point(4) = {7,0,0,1}; 
Point(5) = {15,0,0,1};  
n = 4; // number of intervals
r = 2; // progression  // progression using transfinite mesh  
Point(6) = {0,0.4,0,1}; 
Point(7) = {15,0.4,0,1}; 
Line(1) = {6,7}; 
Transfinite Line {1} = n+1 Using Progression r; 
 // progression using extruded mesh  
a = (r - 1) / (r^n - 1); 
one[0] = 1; 
layer[0] = a; 
For i In {1:n-1}    
one[i] = 1;   
layer[i] = layer[i-1] + a * r^i; 
EndFor 
Point(10) = {0,0.8,0,1}; 
Extrude {15,0,0} {    
Point{10}; 
Layers{one[], layer[]}; }

Ref: http://onelab.info/pipermail/gmsh/2008/003526.html

For some reason, I could not understand what they were trying to explain in the above code, which creates node map using layers to represent a transfinite line using bump. The discussion was about how to use Bump function, but it wasn't clear how to calculate it. There are so many tools for single progression on-line. However, this Bump function isn't clear. Example, if I had the same line and same number of nodes, how would we calculate bump to maintain the same cell size in different blocks.

Any help would be appreciated.

Thanks,

[OpenFoam12]

I was wondering if anyone knows how to calculate grades when using the bump in Gmsh. I have gone through the source code but still unable to get the right grade when the number of nodes as well as the length and first cell height are knowns. So the formula in Gmsh is as follows;

    case 2: // Bump
      {
        double a;
        if(coef > 1.0) {
          a = -4. * sqrt(coef - 1.) * atan2(1., sqrt(coef - 1.)) /
            ((double)nbpt *  length);
        }
        else {
          a = 2. * sqrt(1. - coef) * log(fabs((1. + 1. / sqrt(1. - coef)) /
                                              (1. - 1. / sqrt(1. - coef))))
            / ((double)nbpt * length);
        }
        double b = -a * length * length / (4. * (coef - 1.));
        val = d / (-a * SQU(t * length - (length) * 0.5) + b);
      }

So, the above code shows the equations used when using Bump function for a specified grade. For example,

Transfinite Line {1, 3} = 10 Using Bump 0.8;

In this case, Gmsh will take 0.8, which corresponds to coef, and then calculate "a". "a" in this case supposed to be the first cell height. However, it is not according to my calculations. Anyone knows this formula could provide some insights?

Thanks,

[sz617896964]

Hi,

Have you worked out how to use Bump to calculate the mesh size? I have tried to specify the first layer mesh size (a), the number of points(nbpt) and the length of the line (L). Then, the coefficient can be derived. However, it is incorrect when I use the calculated coefficient and the number of points, as the first layer size is not what I need.

If you have worked out, would you please give some hints to me.

Thanks.