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The gas dynamics under external force field is essentially associated with multiple scale nature due to the large variations of density and local Knudsen number. Single scale fluid dynamic equations, such as the Boltzmann and Navier-Stokes…

Fluid Dynamics · Physics 2017-10-31 Tianbai Xiao , Kun Xu , Qingdong Cai , Tiezheng Qian

The M1 moment model for electronic transport is commonly used to describe non-local thermal transport effects in laser-plasma simulations. In this article, we propose a new asymptotic-preserving scheme based on the Unified Gas Kinetic…

Numerical Analysis · Mathematics 2025-04-09 Jean-Luc Feugeas , Julien Mathiaud , Luc Mieussens , Thomas Vigier

This paper introduces a time-domain harmonic balance unified gas-kinetic scheme (HB-UGKS) designed to simulate temporally periodic flows across all Knudsen regimes. The harmonic balance approach reformulates the periodic problem into a…

Fluid Dynamics · Physics 2026-05-06 Yuze Zhu , Hangkong Wu , Yufeng Wei , Kun Xu

In this paper, a uniformly high-order discontinuous Galerkin gas kinetic scheme (DG-HGKS) is proposed to solve the Euler equations of compressible flows. The new scheme is an extension of the one-stage compact and efficient high-order GKS…

Numerical Analysis · Mathematics 2025-10-14 Mengqing Zhang , Shiyi Li , Dongmi Luo , Jianxian Qiu , Yibing Chen

Parallel algorithms on CPU and GPU are implemented for the Unified Gas-Kinetic Scheme and their performances are investigated and compared by a two dimensional channel flow case. The parallel CPU algorithm has a one dimensional block…

Computational Physics · Physics 2018-11-02 Jizhou Liu , Fang Q. Hu , Xiaodong Li

In this paper, we extend the unified gas-kinetic wave-particle (UGKWP) method to the multi-species gas mixture and multiscale plasma transport. The construction of the scheme is based on the direct modeling on the mesh size and time step…

Computational Physics · Physics 2020-09-21 Chang Liu , Kun Xu

In our study, a compact third order gas-kinetic scheme is constructed for unstructured grid which is combined the compact least-square reconstruction (CLS) method. The CLS method can achieve arbitrary high order compact reconstruction using…

Computational Physics · Physics 2018-02-05 Ji Li , Chengwen Zhong , Congshan Zhuo

With a noticeable increase in research centered on modeling micro fluid interfaces in the framework of mesoscopic methods, we conduct an exhaustive study of discrete unified gas-kinetics scheme (DUGKS) in handling complicated interface…

Computational Physics · Physics 2020-07-16 Zeren Yand , Chengwen Zhong , Congshan Zhuo

In this paper, an efficient high-order gas-kinetic scheme (EHGKS) is proposed to solve the Euler equations for compressible flows. We re-investigate the underlying mechanism of the high-order gas-kinetic scheme (HGKS) and find a new…

Computational Physics · Physics 2020-06-24 Shiyi Li , Yibing Chen , Song Jiang

A dual time-stepping strategy of gas-kinetic scheme for the simulation of unsteady flows is introduced in this work. The dual time-stepping strategy is always used in the approaches of unsteady flows, and the ability of dual time-stepping…

Fluid Dynamics · Physics 2017-05-31 Ji Li , Chengwen Zhong , Yong Wang , Congshan Zhuo

In this paper, we develop a discrete unified gas kinetic scheme (DUGKS) for general nonlinear convection-diffusion equation (NCDE), and show that the NCDE can be recovered correctly from the present model through the Chapman-Enskog…

Computational Physics · Physics 2020-02-19 Jinlong Shang , Zhenhua Chai , Huili Wang , Baochang Shi

In this paper, a unified framework for particulate two-phase flow will be presented with a wide range of solid-particle concentration from dilute to dense limit. The two phase flow is simulated by two coupled flow solvers, i.e., the…

Fluid Dynamics · Physics 2022-02-23 Xiaojian Yang , Wei Shyy , Kun Xu

In this paper, the unified gas-kinetic wave-particle (UGKWP) method has been constructed on three-dimensional unstructured mesh with parallel computing for multiscale flow simulation. Following the direct modeling methodology of the unified…

Computational Physics · Physics 2020-10-28 Yipei Chen , Yajun Zhu , Kun Xu

For the two-layer shallow water equations, a high-order compact gas-kinetic scheme (GKS) on triangular mesh is proposed. The two-layer shallow water equations have complex source terms in comparison with the single layer equations. The main…

Numerical Analysis · Mathematics 2023-06-08 Fengxiang Zhao , Jianping Gan , Kun Xu

This paper presents a highly efficient implicit unified gas-kinetic particle (IUGKP) method for obtaining steady-state solutions of multi-scale phonon transport. The method adapts and reinterprets the integral solution of the BGK equation…

Computational Physics · Physics 2025-06-12 Hongyu Liu , Xiaojian Yang , Chuang Zhang , Xing Ji , Kun Xu

In this paper, we proposed a central moment discrete unified gas-kinetic scheme (DUGKS) for multiphase flows with large density ratio and high Reynolds number. Two sets of kinetic equations with central-moment-based multiple relaxation time…

Fluid Dynamics · Physics 2023-04-05 Chunhua Zhang , Lian-Ping Wang , Hong Liang , Zhaoli Guo

An implicit scheme for steady state solutions of diatomic gas flow is presented. The method solves the Rykov model equation in the finite volume discrete velocity method (DVM) framework, in which the translational and rotational degrees of…

Computational Physics · Physics 2018-11-01 Ruifeng Yuan , Chengwen Zhong

The performance of high-order gas-kinetic scheme (HGKS) has been investigated for the direct numerical simulation (DNS) of isotropic compressible turbulence up to the supersonic regime. Due to the multi-scale nature and coupled…

Computational Physics · Physics 2020-05-19 Guiyu Cao , Liang Pan , Kun Xu

A novel fifth-order compact gas-kinetic scheme is developed for high-resolution simulation of compressible flows on structured meshes. Its accuracy relies on a new multidimensional fifth-order compact reconstruction that uses line-averaged…

Numerical Analysis · Mathematics 2025-08-13 Yaqing Yang , Fengxiang Zhao , Kun Xu

Coherent Rayleigh-Brillouin scattering (CRBS) holds great promise for the characterization of gas properties and the investigation of gas kinetic processes. The CRBS spectrum exhibits a strong dependence on the Knudsen number (Kn),…

Fluid Dynamics · Physics 2025-12-23 Xiaozhe Xi , Junzhe Cao , Kun Xu