On the Discrete Ordinates Method for Non-orthogonal Structured Meshes

Discrete ordinates method has recently been further developed so as to be applicable in orthogonal as well as non-orthogonal, curvilinear coordinate systems. In numerical analysis, complex, irregular regions are mathematically represented by a structured mesh by means of curvilinear coordinate systems. The Radiative Transfer Equation in particular and the Boltzmann Transport Equation in general can be solved efficiently in realistic geometries while employing such techniques. A basic outline of the discrete ordinates method is presented that describes these newly developed techniques. The formalism is applied to two previously published test problems, and the results have been found to be in satisfactory agreement.