Radiation view factors using the Monte-Carlo Ray-Tracing method

1. This example code uses PyVista package to compute geometric parameters and visualize surfaces, normals, etc.
2. Numba JIT compiler is used to improve the performance
3. An example taken from A Frank, et. al.¹. Details of which are shown in the below figure
4. The output of the computed view factors is shown below. We can observe that with 10^6 rays, view factors closely match with the analytical results

view factor from surface 1 to 2 is:
  0.04186
time taken is: 1.880399465560913
view factor matrix:
 [[0.       0.043045 0.294282 0.294431 0.183543 0.184128] 
 [0.042769 0.       0.293895 0.295199 0.183512 0.184435] 
 [0.088093 0.087932 0.       0.452062 0.186441 0.186915] 
 [0.087756 0.087865 0.451547 0.       0.185911 0.186542] 
 [0.091866 0.091742 0.312041 0.312048 0.       0.192414] 
 [0.091341 0.092327 0.311122 0.311516 0.19291  0.      ]] 
time taken is:  44.51021385192871

with compute_vf function time taken is:  31.963478088378906

5. The geometry considered in the above example is
6. The random ray on surface 1 and the normals of surfaces 1 and 2 are shown below

Footnotes

1. A Frank, W Heidemann and K Spindler, Modeling of the surface-to-surface radiation exchange using a Monte Carlo method, Journal of Physics: Conference Series 745 (2016) 032143 ↩