Domain Decomposition Method For Interfacial Heat Transfer Problems With Contact Thermal Resistance

The domain decomposition method can decompose a specific problem into several subproblems,and solve it numerically by exchanging information on the interface,which has unique advantage in dealing with heterogeneous media problems.In this paper,taking the CPU/radiator assembly as an example,a class of interfacial heat transfer problems commonly used in engineering is solved by using the non-overlapping optimized Schwarz method.We divide the problem into two subdomains according to the different materials used in each part of the component,and carry out the information transfer between the subdomains by designing the interface conditions,and optimize the parameters used in the transfer conditions to improve the convergence speed of the algorithm.Firstly,an optimized Schwarz algorithm for the component model is proposed,and the solution when the algorithm converges is proved to be the solution of the original problem,and the convergence factor of the algorithm about the Fourier frequency is obtained by using Fourier analysis as a tool.Next,Robin and twosided Robin transmission conditions are designed,respectively proving the equivalence of the min-max problem of the convergence factor and the equioscillation problem of the convergence factor at the maximum and minimum feasible frequencies in the two cases,because the form of the convergence factor is too complex,it is very difficult to find the optimal parameter expressions corresponding to the two transmission conditions.For the Robin transmission condition,by approximating the convergence factor,we give the expression of the optimal parameter in the steady state,and calculate the relative error of the convergence factor corresponding to the parameter and the original parameter.Aiming at the approximation function of the convergence factor corresponding to two-sided Robin transmission condition,the case where the thermal resistance approaches zero in the steady state is discussed.Secondly,we design the DN algorithm(Dirichlet-Neumann algorithm),and give the expression of the optimal parameter and the expression of the convergence factor in the asymptotic sense.Finally,we carry out numerical experiments to verify the theoretical results of the optimized Schwarz algorithm with Robin and two-sided Robin transmission conditions and the theoretical results of the DN algorithm.The experimental results show that for the optimized Schwarz method,the optimal parameters given by the equioscillation equation can effectively reduce the number of iterations.