Proposition of M3 Method on Multi-Scale Analysis (2nd Report, Formulation of M3 Method for Heat Conduction Problem)

Abstract

In order to reduce the development for the electric device productions, the numerical analysis has been applied well. However, a seamless numerical technique is also required for design, because the modem productions are consist of many components with different size. The multi-scale analysis has been applied to the seamless numerical technique fo these productions. But, the traditional two-scale technique can't adopt, because the differences of size between comportments are very lange. Therefore, M3 method with three-scale technique has been proposed to satisfy the requirements on 1st paper. In this paper, the formulation and a typical example of thermal analysis have been described. Especially, a heat transfer problem under an unsteady state has been analyzed by M3 method and the traditional FEM with fine mesh. A composite material with a particle in the matrix has been treated as a typical example. The numerical results obtained by M3 method have good agreement with the numerical ones obtained by the traditional FEM with fine mesh. It is demonstrated that the distinctions of the rise in temperature and the thermal flow front are generated by the local heterogeneity. In addition, it is revealed that the operation time of mesh generation can reduce dramatically because three scale meshes can generate with the individual operations. From these results, it is recognized that we can reduce the period of the development because M3 method can apply the structure with different size comportments.