A multi-scale method for thermal conduction simulation in granular materials

A multi-scale method is developed to simulate the transient thermal conduction within granular materials consisting of a large number of particles in vacuum. The basic idea of this method is to construct the numerical base functions considering both the topology and the material properties of the particles within the granular system. Dividing the whole domain into a number of coarse elements, the base functions can be accounted from solving the boundary value problem on each element. The thermal conduction and the heat capacity matrices can then be obtained from the contributions of all the contact pairs corresponding to each coarse element. With the global thermal property matrices assembled, the transient thermal conduction problem can be solved using the same technique as the finite element method. Moreover, the temperature of every particle can be simultaneously obtained from the downscaling computation during the computation procedure. The numerical tests indicate that the developed method can be successfully used for solving the transient thermal conduction problem within the granular materials, which can reduce the computational efforts greatly.