Arbitrary polyhedral volume
From CFD-Wiki
Arbitrary Polyhedral Volume
The volume of arbitrary polyhedral can be calculated by using Green-Gauss Theorem.
By choosing the function
Where (x,y,z) are centroid of the surface enclosing the volume under consideration.
As we have,
Hence the volume can be calculated as:
where the normal of the surface pointing outwards is given by:
Final expression could be written as
![volume = \frac{1}{3}\sum\limits_{faces} {\left[ {\left( {x \times n_x + y \times n_y + z \times n_z } \right) \bullet S} \right]}](/W/images/math/7/5/0/750f770a268adfcfe7d6f4019a66fe61.png)
where S is magnitude of Surface Area.
