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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…

数值分析 · 数学 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…

计算物理 · 物理学 2020-05-19 Guiyu Cao , Liang Pan , Kun Xu

For the one-stage third-order gas-kinetic scheme (GKS), success applications have been achieved for the three-dimensional compressible flow computations [33]. The high-order accuracy of the scheme is obtained directly by integrating a…

数值分析 · 数学 2019-02-20 Liang Pan , Kun Xu

Most high order computational fluid dynamics (CFD) methods for compressible flows are based on Riemann solver for the flux evaluation and Runge-Kutta (RK) time stepping technique for temporal accuracy. The main advantage of this kind of…

计算物理 · 物理学 2018-01-17 Xing Ji , Fengxiang Zhao , Wei Shyy , Kun Xu

In this paper, a compact high-order gas-kinetic scheme (GKS) with spectral resolution will be presented and used in the simulation of acoustic and shock waves. For accurate simulation, the numerical scheme is required to have excellent…

计算物理 · 物理学 2020-12-30 Fengxiang Zhao , 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…

数值分析 · 数学 2024-03-04 Yaqing Yang , Liang Pan , Kun Xu

This paper extends the high-order compact gas-kinetic scheme (CGKS) to compressible flow simulations on a rotating coordinate frame. The kinetic equation with the inclusion of centrifugal and Coriolis acceleration is used in the…

计算物理 · 物理学 2022-11-01 Yue Zhang , Xing Ji , Kun Xu

In recent years, coupled with traditional turbulence models, the second-order gas-kinetic scheme (GKS) has been used in the turbulent flow simulations. At the same time, high-order GKS has been developed, such as the two-stage fourth-order…

计算物理 · 物理学 2019-04-04 Guiyu Cao , Hongmin Su , Jinxiu Xu , 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…

流体动力学 · 物理学 2022-08-17 Wenjin Zhao , Guiyu Cao , Jianchun Wang , 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…

数值分析 · 数学 2023-06-08 Fengxiang Zhao , Jianping Gan , 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…

数值分析 · 数学 2025-09-09 Hongyu Liu , Xing Ji , Yuan Fu , Kun Xu

The high-order gas-kinetic scheme (HGKS) has achieved success in simulating compressible flow in Cartesian mesh. To study the flow problem in general geometry, such as the flow over a wing-body configuration, the development of a…

数值分析 · 数学 2024-12-20 Liang Pan , Kun Xu

In this paper, a comparison of the performance of two high-order finite volume methods based on the gas-kinetic scheme (GKS) and HLLC fluxes is carried out in structured rectangular mesh. For both schemes, the fifth-order WENO-AO…

计算物理 · 物理学 2020-09-09 Xiaojian Yang , Xing Ji , Wei Shyy , Kun Xu

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…

数值分析 · 数学 2023-01-25 Yuhang Wang , Guiyu Cao , Liang Pan

A general framework for the development of high-order compact schemes has been proposed recently. The core steps of the schemes are composed of the following. 1). Based on a kinetic model equation, from a generalized initial distribution of…

流体动力学 · 物理学 2022-08-25 Fengxiang Zhao , Xing Ji , Wei Shyy , Kun Xu

In this paper, a high-order gas-kinetic scheme in general curvilinear coordinate (HGKS-cur) is developed for the numerical simulation of compressible turbulence. Based on the coordinate transformation, the Bhatnagar-Gross-Krook (BGK)…

流体动力学 · 物理学 2021-07-20 Guiyu Cao , Kun Xu , Liang Pan , Minping Wan , Shiyi Chen

This paper presents a robust and efficient very high-order scheme for compressible flow simulation, addressing critical limitations of existing high-order methods. The proposed scheme combines the compact gas-kinetic scheme (CGKS) with an…

计算物理 · 物理学 2025-09-04 Junlei Mu , Hong Zhang , Xing Ji , Yang Zhang , Gang Chen , Kun Xu

In this paper, a class of compact higher-order gas-kinetic schemes (GKS) with spectral resolution will be presented. Based on the high-order gas evolution model in GKS, both the interface flux function and conservative flow variables can be…

计算物理 · 物理学 2019-01-03 Fengxiang Zhao , Xing Ji , Wei Shyy , Kun Xu

To meet the demand for complex geometries and high resolutions of small-scale flow structures, a two-stage fourth-order subcell finite volume (SCFV) method combining the gas-kinetic solver (GKS) with subcell techniques for compressible…

数值分析 · 数学 2022-01-05 Chao Zhang , Qibing Li , Peng Song , Jiequan Li

Numerical schemes used for the integration of complex flow simulations should provide accurate solutions for the long time integrations these flows require. To this end, the performance of various high-order accurate numerical schemes is…

流体动力学 · 物理学 2012-12-06 Omer San , Anne E. Staples
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