Solid angle is much, much farther away. The solid angle subtended by the complete ()-dimensional spherical surface of the unit sphere in -dimensional Euclidean space can be defined in any number of dimensions . One often needs this solid angle factor in calculations with spherical symmetry. It is given by the formula where is the gamma function. When is an integer, the gamma function can be computed explicitly. It follows that This gives the expected results of 4 steradians for the 3D sphere bounded by a surface of area and 2 radians for the 2D circle bounded by a circumference of length
Finite volume method tensor. Again we can sub-divide the spatial domain into finite volumes or cells. For a particular cell, formula_42, we take the volume integral over the total volume of the cell, formula_43, which gives, On integrating the first term to get the "volume average" and applying the "divergence theorem" to the second, this yields where formula_46 represents the total surface area of the cell and formula_47 is a unit vector normal to the surface and pointing outward. So, finally, we are able to present the general result equivalent to (8), i.e. Again, values for the edge fluxes can be reconstructed by