DISCRETE ORDINATES QUADRATURE SCHEMES FOR MULTIDIMENSIONAL RADIATIVE-TRANSFER

The fundamental problem of applying the method of discrete ordinates to radiative transfer predictions is the selection of the discrete directions and their associated weights. Both the accuracy of the solution and the computational effort depend on the angular discretization. This paper provides a sound mathematical methodology for the derivation of angular quadratures. By applying the collocation principle, the errors introduced by a quadrature are analysed and the constituting equations of angular quadratures are identified. Special emphasis is placed on the rotational invariance of the quadrature schemes. Multidimensional radiative transfer in participating media with isotropic and anisotropic scattering is accounted for thoughout the analysis. A major goal of the present study is the construction of a new principle for multidimensional angular quadratures which is essentially a generalization of the principles employed for the well-known S-n quadratures. The new construction principle has two major advantages. First, it enables a very flexible tailoring of quadratures according to the actual requirements. Second, compared to the S-n quadratures, the new types of quadratures provide a higher accuracy while using the same number of nodal points.