Following from: Discrete ordinates and finite volume methods
Discrete Form of the Governing Equations
The mathematical formulation of the discrete ordinates method (DOM) and finite volume method (FVM) has been presented in the article “Mathematical formulation.” In that article, it was shown that, in the case of Cartesian coordinates, and when the step scheme is employed, the discretized equations for the DOM may be written as follows for a control volume centered at grid node P:
for m = 1, 2, ... M. If the FVM is used, the corresponding discretized equations take the following form:
for m = 1, 2, ... M. In both cases, the equations may be rewritten as follows:
where the summation extends over all the neighbors of grid node P, which will be denoted as E (east), W ( ...