Yajun Zhu

Chang Liu, Yajun Zhu, Kun Xu

The unified gas-kinetic scheme (UGKS) provides a framework for simulating multiscale transport with the updates of both gas distribution function and macroscopic flow variables on the cell size and time step scales. The multiscale dynamics in UGKS is achieved through the coupled particle transport and collision in the particle evolution process within a time step. In this paper, under the UGKS framework, we propose an efficient multiscale unified gas-kinetic wave-particle (UGKWP) method. The gas dynamics in UGKWP method is described by the individual particle movement coupled with the evolution of the probability density function (PDF). During a time step, the trajectories of simulation particles are tracked until collision happens, and the post-collision particles are evolved collectively through the evolution of the corresponding distribution function. The evolution of simulation particles and distribution function is guided by evolution of macroscopic variables. The two descriptions on a gas particle, i.e. wave and particle, switch dynamically with time. A new concept of multiscale multi-efficiency preserving (MMP) method is introduced, and the UGKWP method is shown to be an MMP scheme. The UGKWP method is specially efficient for hypersonic flow simulation in all regimes in comparison with the wave-type discrete ordinate methods, and presents a much lower stochastic noise in the continuum flow regime in comparison with the particle-based Monte Carlo methods. Numerical tests for flows over a wide range of Mach and Knudsen numbers are presented. The examples include mainly the hypersonic flow passing a circular cylinder at Mach numbers $20$ and $30$ and Knudsen numbers $1$ and $10^{-4}$, low speed lid-driven cavity flow, and laminar boundary layer. These results validate the accuracy, efficiency, and multiscale property of UGKWP method.

Weiming Li, Chang Liu, Yajun Zhu et al.

In this work, we present a unified gas-kinetic particle (UGKP) method for the simulation of multiscale photon transport. The multiscale nature of the particle method mainly comes from the recovery of the time evolution flux function in the unified gas-kinetic scheme (UGKS) through a coupled dynamic process of particle transport and collision. This practice improves the original operator splitting approach in the Monte Carlo method, such as the separated treatment of particle transport and collision. As a result, with the variation of the ratio between numerical time step and local photon's collision time, different transport physics can be fully captured in a single computation. In the diffusive limit, the UGKP method could recover the solution of the diffusion equation with the cell size and time step being much larger than the photon's mean free path and the mean collision time. In the free transport limit, it presents an exact particle tracking process as the original Monte Carlo method. In the transition regime, the weights of particle free transport and collision are determined by the ratio of local numerical time step to the photon's collision time. Several one-dimensional numerical examples covering all transport regimes from the optically thin to optically thick are computed to validate the accuracy and efficiency of the current scheme. In comparison with the $S_N$ discrete ordinate method, the UGKP method is based on particles and avoids the discretization of particle velocity space, which does not suffer from the ray effect.