Phonon Boltzmann equation-based discrete unified gas kinetic scheme for multiscale heat transfer

TL;DR

This paper introduces a discrete unified gas kinetic scheme based on the phonon Boltzmann equation, capable of accurately modeling multiscale heat transfer across diffusive and ballistic regimes with adaptive features.

Contribution

The work develops a second-order finite-volume DUGKS for phonon transport that is asymptotic preserving and effective across multiple heat transfer regimes.

Findings

Accurately predicts heat transfer in diffusive and ballistic regimes.

Demonstrates effectiveness through numerical tests with various Knudsen numbers.

Provides a self-adaptive multiscale modeling approach.

Abstract

Numerical prediction of multiscale heat transfer is a challenging problem due to the wide range of time and length scales involved. In this work a discrete unified gas kinetic scheme (DUGKS) is developed for heat transfer in materials with different acoustic thickness based on the phonon Boltzmann equation. With discrete phonon direction, the Boltzmann equation is discretized with a second-order finite-volume formulation, in which the time-step is fully determined by the Courant-Friedrichs-Lewy (CFL) condition. The scheme has the asymptotic preserving (AP) properties for both diffusive and ballistic regimes, and can present accurate solutions in the whole transition regime as well. The DUGKS is a self-adaptive multiscale method for the capturing of local transport process. Numerical tests for both heat transfers with different Knudsen numbers are presented to validate the current method.