Fast Multipole Boundary Element Method For Coupled Radiation-conduction Heat Transfer Problem

The coupled radiation and conduction heat transfer exists widely in various engineering applications with high temperatures.Analytical solution to such coupled heat transfer system is almost unavailable due to complex mathematical model.In the past decades,the research on its numerical solutions has been a fascinating area of research.This thesis mainly focuses on the boundary element method(BEM)and fast multipole boundary element method(FMBEM)for this coupled heat transfer problem,and these algorithms are applied to solve some classical numerical examples.The main contents and research results of this thesis include the following aspects:1.For the radiative integral transfer system in three-dimensional semitransparent media,the boundedness of the four radiative integral operators is first analyzed and proved theoretically.Based on these properties and the principle of contraction mapping,the existence and uniqueness of the solution to the integral system is proved.Besides,the convergence of an iterative scheme is also analyzed and proved.For the problem of thermal radiation in non-convex region,a high-precision shadow detection algorithm is developed and combined with the collocation scheme based on boundary element method to solve the integral system.The numerical results of this hybrid algorithm are compared with those in the literatures.The results show that the algorithm developed in this thesis is of high accuracy and high efficiency.2.For the coupled radiation-conduction heat transfer in three-dimensional inhomogeneous semitransparent media,a simple variable transformation is used to transform the nonlinear energy equation with variable coefficients into a nonlinear equation with constant coefficients.The Newton iterative scheme is used to linearize the transformed nonlinear equation.For the radiative integral transfer equations in a nonhomogeneous semitransparent media with isotropic scattering,the iterative scheme in the previous part is used.Hence,a two-level iterative scheme is used to solve the coupled radiation-conduction heat transfer in three-dimensional inhomogeneous semitransparent media.The boundary element method based on collocation scheme is used to discretize the whole system.The numerical results show the effectiveness of the proposed algorithm.3.For the radiative integral transfer system in three-dimensional semitransparent media,a kernel-independent fast multipole boundary element method(KIFMBEM)based on the generalized minimal residual(GMRES)iterative solver is developed.The participating media is absorbing-emitting-isotropic scattering.Since it is not necessary to store the coefficient matrix of the discrete system,the integral system is solved by direct method.The conventional boundary element method based on collocation scheme is used to discretize the integral system.The numerical results are compared with those of the classical literatures and those of the conventional boundary element method.It is shown that the KIFMBEM developed in this thesis is an accurate and efficient numerical algorithm.4.For the coupled radiation-conduction heat transfer in three-dimensional semitransparent media,a KIFMBEM based on the GMRES iterative solver is developed.Unlike the work in the second part,a single-level iterative scheme is applied to the whole system.The boundary element method based on collocation scheme is used to discretize both thermal radiation and thermal conduction,and the GMRES is used to solve each part of the algebraic system.In each iteration,the kernel-independent fast multipole algorithm is used to accelerate the matrix-vector product.The numerical results from the present method are compared with those of the conventional boundary element method.It is demonstrated that the fast algorithm developed in this thesis greatly improves computational efficiency at the expense of minimal precision.