Application Of Multi-domain Boundary Face Method In 3D Transient Heat Conduction Problems

Since boundary face method(BFM) has many advantages, for instance it can obtain high accuracy; it is suitable for solving problems involving infinite domains and singularity, moreover, it can make the integration of CAD/CAE possible. the paper studies the application of the BFM in analysis of transient heat conduction problem of three dimensional structure, including single-domain structures and large scale multi-domain structure, which is composed of a variety of materials and required parallel computing.Firstly, The paper introduces the derivation of control equations of transient heat conduction problems, the derivation of boundary integral equation, algorithms for solving boundary integral equation and their respective advantages and disadvantages. Considering that quasi-initial condition method has the advantages of high computational efficiency and using less computer resource, we mainly introduce the process of the numerical implementation of the boundary integral equation using the quasi-initial condition method.Secondly, in view of the fact that nearly singular integral is difficult to solve and the calculation result is very low, this paper presents a novel subdivision method, which is called Sphere Subdivision. The algorithm is divided in physical coordinates, through a series of point source intersection of cutting unit for spherical and unit circle radius, shrinking, and the cycle of the process, the final completion of the segmentation unit. With source distance reduced, integral tablets will continue to automatically refine, to ensure close to the source point can also be obtained by the shape and size of ideals, integral piece to Gauss integral. This method improves the accuracy and efficiency of the integral considerably.Thirdly, in order to apply the BFM to transient heat conduction problem in multi domain structure, we extend the BFM to multi domain boundary face method on the basis of the boundary integral equation. In this paper, we take a two-domain model as an example to present the assembly of the matrices in multi-domain matrix. To solve the multi domain structure, boundary integral equations for each sub domain should be established first. Then the boundary integral equations for each sub domain are assembled into one equation using the equilibrium condition and compatibility condition. The sparse matrix of each sub domain is full rank matrix, but the matrix obtained by assembly is partitioned matrix, and that makes the solving process much simpler. At the same time, the computational efficiency is improved.At last, the paper gives several examples with different boundary conditions to prove the feasibility and accuracy of applying the BFM to analysis of transient heat conduction problems of three dimensional structures. These structures include singledomain structures and large scale multi-domain structures, some of which are composed of a variety of materials. The comparison of the results with FEM presents that the multi-domain BFM has feasibility and some advantages in the application of heat conduction problems.