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High-order gas-kinetic scheme (HGKS) has become a workable tool for the direct numerical simulation (DNS) of turbulence. In this paper, to accelerate the computation, HGKS is implemented with the graphical processing unit (GPU) using the…

Numerical Analysis · Mathematics 2023-01-25 Yuhang Wang , Guiyu Cao , Liang Pan

In this paper, we present an advanced high-order compact gas-kinetic scheme (CGKS) for 3D unstructured mixed-element meshes, augmented with a geometric multigrid technique to accelerate steady-state convergence. The scheme evolves…

Computational Physics · Physics 2024-02-06 Hongyu Liu , Xing Ji , Yunpeng Mao , Yuan Ding , Kun Xu

Implicit methods and GPU parallelization are two distinct yet powerful strategies for accelerating high-order CFD algorithms. However, few studies have successfully integrated both approaches within high-speed flow solvers. The core…

Numerical Analysis · Mathematics 2025-09-09 Hongyu Liu , Xing Ji , Yuan Fu , Kun Xu

In the previous studies, the high-order gas-kinetic schemes (HGKS) have achieved successes for unsteady flows on three-dimensional unstructured meshes. In this paper, to accelerate the rate of convergence for steady flows, the implicit…

Numerical Analysis · Mathematics 2024-03-05 Yaqing Yang , Liang Pan , Kun Xu

In recent years, non-equilibrium flows have gained significant attention in aerospace engineering and micro-electro-mechanical systems. The unified gas-kinetic scheme (UGKS) follows the methodology of direct modeling to couple particle…

Computational Physics · Physics 2024-12-10 Yue Zhang , Yufeng Wei , Wenpei Long , Kun Xu

This paper presents a Graphics Processing Units (GPUs) acceleration method of an iterative scheme for gas-kinetic model equations. Unlike the previous GPU parallelization of explicit kinetic schemes, this work features a fast converging…

Computational Physics · Physics 2020-01-08 Lianhua Zhu , Peng Wang , Songze Chen , Zhaoli Guo , Yonghao Zhang

The unified gas kinetic scheme (UGKS) is a direct modeling method based on the gas dynamical model on the mesh size and time step scales. With the implementation of particle transport and collision in a time-dependent flux function, the…

Computational Physics · Physics 2017-10-25 Yajun Zhu , Chengwen Zhong , 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

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

In this paper, the high-order compact gas-kinetic scheme (CGKS) on three-dimensional hybrid unstructured mesh is further developed with the p-multigrid technique for steady-state solution acceleration. The p-multigrid strategy is a…

Computational Physics · Physics 2021-09-22 Xing Ji , Wei Shyy , Kun Xu

For the simulations of unsteady flow, the global time step becomes really small with a large variation of local cell size. In this paper, an implicit high-order gas-kinetic scheme (HGKS) is developed to remove the restrictions on the time…

Numerical Analysis · Mathematics 2024-03-04 Yaqing Yang , Liang Pan , Kun Xu

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

The recent trend of using Graphics Processing Units (GPU's) for high performance computations is driven by the high ratio of price performance for these units, complemented by their cost effectiveness. At first glance, computational fluid…

Computational Engineering, Finance, and Science · Computer Science 2018-02-13 Kiril S. Shterev

The trade-off among accuracy, robustness, and computational cost remains a key challenge in simulating complex flows. Second-order schemes are computationally efficient but lack the accuracy required for resolving intricate flow structures,…

Numerical Analysis · Mathematics 2025-08-28 Yaqing Yang , Fengxiang Zhao , Kun Xu

Unstructured meshes present challenges in scientific data analysis due to irregular distribution and complex connectivity. Computing and storing connectivity information is a major bottleneck for visualization algorithms, affecting both…

Distributed, Parallel, and Cluster Computing · Computer Science 2025-08-01 Guoxi Liu , Thomas Randall , Rong Ge , Federico Iuricich

This paper presents the benchmarking and scaling studies of a GPU accelerated three dimensional compressible magnetohydrodynamic code. The code is developed keeping an eye to explain the large and intermediate scale magnetic field…

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

The unified gas-kinetic scheme (UGKS) is a direct modeling method for multiple scale transports. The modeling scale of the scheme is the mesh size and time step, and the ratios of the mesh size over particle mean free path or the time step…

Computational Physics · Physics 2019-05-01 Yajun Zhu , Chengwen Zhong , Kun Xu

Simulating multiscale flows with moving boundaries, such as hypersonic multi-body separation and flows in micro-electro-mechanical systems (MEMS), requires robust numerical methods that couple mesh deformation with complex flow physics.…

Fluid Dynamics · Physics 2026-04-14 Yue Zhang , Wenpei Long , Junzhe Cao , Kun Xu

High-order gas-kinetic scheme (HGKS) with 5th-order non-compact reconstruction has been well implemented for implicit large eddy simulation (ILES) in nearly incompressible turbulent channel flows. In this study, the HGKS with higher-order…

Fluid Dynamics · Physics 2022-08-17 Wenjin Zhao , Guiyu Cao , Jianchun Wang , Kun Xu
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