This article reviews rarefied gas flow computations based on nonlinear model Boltzmann
equations using deterministic high-order gas-kinetic unified algorithms (GKUA) in phase …

In this survey we consider the development and mathematical analysis of numerical
methods for kinetic partial differential equations. Kinetic equations represent a way of …

Computational fluid dynamics (CFD) studies the flow motion in a discretized space. Its basic
scale resolved is the mesh size and time step. The CFD algorithm can be constructed …

Recently, as aerodynamics was applied to flying vehicles with very high speed and flying at
high altitude, the numerical simulation based on the Navier–Stokes (NS) equations was …

One of the central problems in the study of rarefied gas dynamics is to find the steady-state
solution of the Boltzmann equation quickly. When the Knudsen number is large, ie the …

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 …

In the study of rarefied gas dynamics, the discrete velocity method (DVM) has been widely
employed to solve the gas kinetic equations. Although various versions of DVM have been …

Based on the fast spectral approximation to the Boltzmann collision operator, we present an
accurate and efficient deterministic numerical method for solving the Boltzmann equation …

A unified gas-kinetic scheme (UGKS) is constructed for both continuum and rarefied flow
computations. The underlying principle for the development of UGKS is the direct modeling …

The apparent gas permeability of a porous medium is an important parameter in the
prediction of unconventional gas production, which was first investigated systematically by …