An implicit gas-kinetic scheme for turbulent flow on unstructured hybrid mesh

Pan, Dongxin; Zhong, Chengwen; Zhuo, Congshan

doi:10.1016/j.camwa.2018.02.032

Cited by 6 publications

(2 citation statements)

References 28 publications

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“…The implicit scheme can not only increase the convergence efficiency but also improve the numerical stability, which is also vital for high-speed flow simulations. The implicit and multigrid acceleration techniques have been developed in the GKS as well for fast solving of both steady and unsteady state problems [3,[26][27][28][29][30][31][32][33].…”

Section: Implicit Scheme and Multigrid Accelerationmentioning

confidence: 99%

“…Another distinguishable feature of the GKS is the multi-dimensional property of the flux function [3,8], which incorporates both normal and tangential variations of the flow field in the flux computation, and makes the GKS suitable for flow simulations on unstructured mesh. In order to simulate high-speed flow, the GKS has been further developed in the aspects of physical modeling and numerical algorithms, such as the kinetic boundary condition [9,10], multiple temperature model [11][12][13][14][15][16][17][18][19][20], multi-component and reactive flow [21][22][23][24][25], and implicit scheme and multigrid acceleration [3,[26][27][28][29][30][31][32][33]. By employing a modified relaxation time [10,13,34], the corresponding constitutive relationship in the GKS have been improved so that the GKS can be applied in the near continuum regime.…”

Section: Introductionmentioning

confidence: 99%

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GKS and UGKS for High-Speed Flows

Zhu

Zhong

2021

Aerospace

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The gas-kinetic scheme (GKS) and the unified gas-kinetic scheme (UGKS) are numerical methods based on the gas-kinetic theory, which have been widely used in the numerical simulations of high-speed and non-equilibrium flows. Both methods employ a multiscale flux function constructed from the integral solutions of kinetic equations to describe the local evolution process of particles’ free transport and collision. The accumulating effect of particles’ collision during transport process within a time step is used in the construction of the schemes, and the intrinsic simulating flow physics in the schemes depends on the ratio of the particle collision time and the time step, i.e., the so-called cell’s Knudsen number. With the initial distribution function reconstructed from the Chapman–Enskog expansion, the GKS can recover the Navier–Stokes solutions in the continuum regime at a small Knudsen number, and gain multi-dimensional properties by taking into account both normal and tangential flow variations in the flux function. By employing a discrete velocity distribution function, the UGKS can capture highly non-equilibrium physics, and is capable of simulating continuum and rarefied flow in all Knudsen number regimes. For high-speed non-equilibrium flow simulation, the real gas effects should be considered, and the computational efficiency and robustness of the schemes are the great challenges. Therefore, many efforts have been made to improve the validity and reliability of the GKS and UGKS in both the physical modeling and numerical techniques. In this paper, we give a review of the development of the GKS and UGKS in the past decades, such as physical modeling of a diatomic gas with molecular rotation and vibration at high temperature, plasma physics, computational techniques including implicit and multigrid acceleration, memory reduction methods, and wave–particle adaptation.

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Section: Implicit Scheme and Multigrid Accelerationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

GKS and UGKS for High-Speed Flows

Zhu

Zhong

2021

Aerospace

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Multi-degree-of-freedom kinetic model and its applications in simulation of three-dimensional nonequilibrium flows

et al. 2023

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A two-stage fourth-order gas-kinetic scheme on unstructured hybrid mesh

Pan

Zhong

Zhuo

et al. 2019

Computer Physics Communications

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This paper presents an accurate and robust fourth order gas-kinetic scheme on two dimensional unstructured hybrid mesh for incompressible and compressible viscous flows. For generalized Riemann problem and Navier-Stokes solution, the gas-kinetic scheme (GKS) provides a time-accurate flux solver using a different way in the reconstruction at a cell interface in which two slopes for the equilibrium state are used. Different from the previous onestage time-stepping method, the two-stage Lax-Wendroff type time stepping method is applied in this paper. Compared to standard four-stage fourthorder Runge-Kutta method, the two-stage fourth order time accurate method reduces the complexity of the adoption of time derivative of the flux function. To achieve fourth order accuracy, a finite volume method for GKS using cubic spline reconstruction is proposed on both structured grid and unstructured hybrid mesh. When dealing with flow discontinuities, the original spline scheme is replaced by the one blended with shock-capturing WENO scheme. Many one and two-dimensional test cases, including Couette flow, Shu-Osher problem, Woodward-Colella blast problem, two-dimensional Riemann problem, viscous shock tube flow, supersonic flow over a forward-facing step, and hypersonic flow over a circular cylinder, are carried out to demonstrate the performance of the proposed scheme.

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An implicit gas-kinetic scheme for turbulent flow on unstructured hybrid mesh

Cited by 6 publications

References 28 publications

GKS and UGKS for High-Speed Flows

GKS and UGKS for High-Speed Flows

Multi-degree-of-freedom kinetic model and its applications in simulation of three-dimensional nonequilibrium flows

A two-stage fourth-order gas-kinetic scheme on unstructured hybrid mesh

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