The motivation of the current paper is to provide a detailed review of crucial topics in micro-
and nanoscale gas flows, ie, velocity slip and temperature jump phenomena and their …

Over the past half century, a variety of computational fluid dynamics (CFD) methods and the
direct simulation Monte Carlo (DSMC) method have been widely and successfully applied to …

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 …

In this study, we propose a non-linear continuous stochastic velocity process for simulations
of monatomic gas flows. The model equation is derived from a Fokker–Planck approximation …

In this paper, we present a unified gas-kinetic wave-particle (UGKWP) method on
unstructured mesh for the multiscale simulation of continuum and rarefied flow. Inheriting …

The stochastic particle method based on Bhatnagar-Gross-Krook (BGK) or ellipsoidal
statistical BGK (ESBGK) model approximates the pairwise collisions in the Boltzmann …

Recently, a unified stochastic particle (USP) method [14] has been developed for the
simulation of multiscale nonequilibrium gas flows. Compared with the conventional …

In this paper, a new time-relaxed Monte Carlo (TRMC) method is proposed for the
inhomogeneous Boltzmann equation. Compared to the standard TRMC scheme, the …

The whole picture of Mathematical Modeling is systematically and thoroughly explained in
this text for undergraduate and graduate students of mathematics, engineering, economics …

A Fokker–Planck based particle Monte Carlo algorithm was devised recently for simulations
of rarefied gas flows by the authors [1],[2],[3]. The main motivation behind the Fokker–Planck …