AN EFFICIENT ALGORITHM FOR CALCULATING MULTIPARTICLE THERMAL INTERACTION IN A CONCENTRATED DISPERSION OF SPHERES

The boundary-value problem of heat conduction through a multiparticle system in a medium of a different conductivity lambda(e) is considered , The particle set is a random arrangement of N equisized spheres of c onductivity lambda' in a cubic cell continued periodically into all sp ace. The mean temperature gradient is given. The problem is reduced to an infinite set of equations for the coefficients of the temperature expansion into spherical harmonics on the interfaces. The algorithm ex ploits the idea that only the interaction of the low-frequency harmoni cs is long-ranged to construct the ''economical truncation,'' as well as the rotational transformations of spherical harmonics to promote th e efficient iterative solution. The method is capable of providing hig h resolution for arbitrary conductivity ratio gamma = lambda'/lambda(e ) and enabling large scale simulations of the effective conductivity o f highly concentrated dispersions with various microstructures even on a small computer. (C) 1994 Academic Press, Inc