Unified gas-kinetic wave-particle method for multi-scale phonon transport

Over the past 7 decades, the classical Monte Carlo method has played a huge role in the fields of rarefied gas flow and micro/nano scale 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 multi-scale 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 multi-scale flux at the cell interfaces. At the same time, in order to capture non-equilibrium transport efficiently, the multi-scale flux comprises two distinct components: a deterministic part for capturing the near-equilibrium or diffusive transport and a statistical particle part for recovering non-equilibrium or ballistic transport phenomena. The UGKWP method exhibits remarkable multi-scale adaptability and versatility, seamlessly bridging the gap between the diffusive and ballistic transport phenomena. In the diffusive limit, the present method naturally converges to the Fourier's law, with the diminishing particle contribution, whereas in the ballistic limit, the non-equilibrium flux is fully described by the free-streaming particles. This inherent adaptability not only allows for precise capturing of both equilibrium and non-equilibrium heat transfer processes but also guarantees that the model adheres strictly to the underlying physical laws in each phonon transport regime.