Unified gas-kinetic wave-particle method for multiscale phonon transport.

Abstract

Over the past seven decades, the classical Monte Carlo method has played a huge role in the fields of rarefied gas flow and micro/nanoscale heat transfer, but it also has shortcomings: the time step and cell size are limited by the relaxation time and mean free path, making it difficult to efficiently simulate multiscale heat and mass transfer problems from the ballistic to diffusion limit. To overcome this drawback, a unified gas-kinetic wave-particle (UGKWP) method is developed for solving the phonon Boltzmann transport equation (BTE) in all regimes covering both ballistic and diffusive limits. This method is built upon the space-time coupled evolution model of the phonon BTE, which provides the framework for constructing a multiscale flux at the cell interfaces. At the same time, in order to capture nonequilibrium transport efficiently, the multiscale flux comprises two distinct components: a deterministic part for capturing the near-equilibrium or diffusive transport, and a statistical particle part for recovering nonequilibrium or ballistic transport phenomena. The UGKWP method exhibits remarkable multiscale adaptability and versatility, seamlessly bridging the gap between the diffusive and ballistic transport phenomena. In the diffusive limit, the present method naturally converges to Fourier's law, with the diminishing particle contribution, whereas in the ballistic limit, the nonequilibrium flux is fully described by the free-streaming particles. This inherent adaptability not only allows for precise capturing of both equilibrium and nonequilibrium heat transfer processes, but it also guarantees that the model adheres strictly to the underlying physical laws in each phonon transport regime. A series of numerical tests fully demonstrate the excellent performance of the UGKWP method in all Knudsen regimes, where the time step and cell size are not constrained by the relaxation time and mean free path in the diffusive regime. The present method is an efficient and accurate computational tool for simulating multiscale nonequilibrium heat transfer, and offering significant advantages over traditional methods in terms of numerical performance and physical applicability.