FA Method on Diagonal Cartesian Coordinates

The diagonal Cartesian method uses both Cartesian grid lines and diagonal line segments to approximate complex geometry. The 9-point finite analytic (FA) discretization is used on the rectangular elements. However, the triangular elements include only five nodes, so the 9-point FA coefficient formulas do not apply. This chapter is devoted to the development of the 5-point FA method for use on the triangular cells. The three-dimensional transport equation must be discretized on each of the resulting diagonal Cartesian cells used in approximating a complex three-dimensional domain. A cell near the surface boundary of the complex three-dimensional domain may have one or more planes that intersect with the boundary. If so, the resulting intersection is a curve in the given plane, and the curve is approximated using the Cartesian segments or the diagonal.