XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX''"> 8.2 Viewfactor
The finite element model for the viewfactor associated with the ith node on surface e to the jth node on surface f is represented by the following formula:
(8‑1)
subject to the restrictions that
does not intersect any view obstructing surfaces and the product
is negative, and
e | = | Surface e ID |
f | = | Surface f ID |
i | = | Node ID on surface e |
j | = | Node ID on surface f |
Ae | = | Surface e area |
Af | = | Surface f area |
| = | Primary variable finite element interpolation function associated with the ith node on surface e |
| = | Vector from a point on surface e to a point on surface f |
| = | Unit normal to surface e |
| = | Magnitude of a vector |
The right-hand side of this equation is evaluated using numerical methods. The numerical integration scheme is predominantly Gaussian quadrature. The quadrature order may be varied by the Viewfactor analysis program in an attempt to obtain the desired accuracy. The method for estimating the accuracy of the numerical integration is, of course, empirical, but seems to work very well. In general, if sufficient accuracy has not been obtained, then the quadrature order will be increased in an effort to improve the accuracy. The quadrature order is not increased globally throughout the integration domain, but only in those areas where the program determines the most benefit will result.
