Meshless Method For Solving Radiative Transfer Equation

Many approximation methods have been proposed to solve radiative heat transfer problem in semitransparent media. These methods can be divided into two types. One is the methods based on the ray-tracing technique, such as Monte-Carlo method, zone method, discrete transfer method; the other is methods based on the discretization of radiative transfer equation, such as discrete ordinate method, finite volume method, finite element method and so on. These traditional methods need to generate the mesh in problem domain. To the problems with changing boundaries, such as fire hazard, combustion in cylinder, the traditional methods must suffer from the drawbacks of tedious process in meshing and remeshing. Meshless method is a new method, which uses a set of points to discretize the problem domain. Compactly supported function is used to construct the trial function, and weighted residual method with compactly supported function is employed to discretize the differential equation. The Meshless method is very suitable for solving the problem with changing boundaries.In this dissertation, meshless method has been employed to solve the radiative heat transfer problems in participating media. Numerical characteristic parameters of meshless method have been investigated in solving radiative heat transfer problem. Meshless method is also extended to solve the transient radiative transfer equation.The main work includes the following four aspects of investigations.1. Meshless local Petrov-Galerkin method (MLPG) is developed for solving the raidative heat transfer problems in homogeneous medium. A moving least-square approach is employed to construct the trial function. The MLPG approach for radiative transfer is based on the discrete ordinate equations. Particular test cases for radiative heat transfer are examined to check the method. The best combination of size parameters of supported domain and sub-domain is obtained. Upwind scheme is developed to eliminate the instability of solutions obtained by using MLPG approach.2. Least-square collocation meshless (LSCM) method has been extended to solve...