Implementation of the P_N-Approximation for Radiative Heat Transfer on OpenFOAM

This work presents an OpenFOAM implementation of the P_N approximation for radiative heat transfer, including higher orders P₃, P₅, and P₇. Also described is a procedure which enables the sequential numerical computations of the coupled partial differential equations (PDEs) by re-expressing the boundary conditions in matrix form so that individual boundary conditions can be associated with each PDE. The implementation of the software programs are verified with derived analytical solutions for 1-D slabs with constant and variable properties, and are also tested with various orientations in order to demonstrate the geometric invariance properties of the 3-dimensional P_N formulation. A few examples taken from the literature are also considered in this work and could be taken as benchmark solutions for the P_N approximations.