A fast coupled solver for phonon transport in composites

In recent years, computational techniques for solving phonon transport have been developed under the framework of the semiclassical Boltzmann Transport Equation (BTE). Early work addressed gray transport, but more recent work has begun to resolve wave vector and polarization dependence, including that in relaxation times. Because the relaxation time in typical materials of interest spans several orders of magnitude, typical solution techniques must address an enormous range of Knudsen numbers in the same problem. Calculation procedures which solve the BTE in phase space sequentially work well in the ballistic limit, but are slow to converge in the thick limit. Unfortunately, both extremes may be encountered simultaneously in typical wave-number (K) -resolved phonon transport problems. In previous work, we developed the coupled ordinate method (COMET) to address this problem. COMET employs a point-coupled solution to resolve coupling in K-space, and embeds this point solver as a relaxation sweep in a geometric multigrid method to maintain spatial coupling. We have demonstrated speedups of up to 200 over conventional sequential solution procedures using this method. COMET also exhibits excellent scaling on multiprocessor platforms, far beyond those obtained by sequential solvers.In this paper, we extend COMET to address interface transport in composites. Just as scattering couples phonons of different wave vectors in the bulk, reflection and transmission couple different wave vectors together at interfaces. Again, sequential solution procedures perform poorly because of the poor algorithmic coupling in K space. A computational procedure based on COMET is developed for composites, addressing multigrid agglomeration strategies to promote stronger K-space coupling at interfaces. The technique is applied to canonical superlattice geometries and superior performance over typical sequential solvers is demonstrated. Furthermore, the method is applied to realistic particle composites employing computational meshes developed from x-ray computed tomography (CT) scans of particulate beds. It is demonstrated to yield solutions where sequential solution techniques fail to converge at all.Copyright © 2013 by ASME