Surface area Surface area The surface area of a solid object is a measure of the total area that the surface of the object occupies. The mathematical definition of surface area in the presence of curved surfaces is considerably more involved than the definition of arc length of one-dimensional curves, or of the surface area for polyhedra (i.e., objects with flat polygonal faces), for which the surface area is the sum of the areas of its faces. Smooth surfaces, such as a sphere, are assigned surface area using their representation as parametric surfaces. This definition of surface area is based on methods
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