Simulation Of The Spherical Harmonics Method For Radiative Transfer

As one of the three forms of heat transfer, radiation plays an important role in engineering,and solving RTE is a hot topic. After nearly a hundred years,a variety of numerical methods of radiative heat transfer have been developed with advantages and disadvantages as well. Radiative transfer equation is an integro-differential equation,which includes both the differential coordinates of space and the direction of the integration of space.Therefore, not only the spatial dispersion should be done,but also the direction of space needs proper treatment for the numerical simulation of radiative transfer.Spherical harmonics (P_N-approximation) ,which separate the spatial location and direction of changes, using the orthogonality of spherical harmonics without discrecting the solid angles, transforme the raditive transfer equation into a set of simple partial differential equations. we can obtain radiative intensity in any direction.However,high-order P_N-approximations quickly become tedious ,even for simple geometries.Therefore, The current study focused on P₁-approximation and P₃-approximation.In this dissertation ,the model for radiation transfer of one-dimensional and two-dimensional retangular plat medium is set up.In order to solve these prombers,the basic studies are as followed:1. The model of one-dimension and two-dimensional retangular plat paticipating media for P₁-approximation and P₁-FEM is bulit, and the opaque diffuse boundary conditions as well.2. The model of one-dimensional slab and two-dimensional retangular plat paticipating media with black and gray boundaries for P₃-approimation is presented.3. Calculate P₁ and P₃ approximation under radiation non-equilibrium and equilibrium for one-dimensional slab and two-dimensional retangular plat. Discussing the effect of optical thickness on accuracy.Compare it under the same circumstances and recommend the using conditions.