A multi-prediction implicit scheme for steady state solutions of gas flow in all flow regimes

Yuan, Ruifeng; Liu, Sha; Zhong, Chengwen

doi:10.1016/j.cnsns.2020.105470

Cited by 27 publications

(10 citation statements)

References 39 publications

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“…Based on the multi-scale property of the UGKS flux, we can naturally take the viscosity flux into account and use the viscous solution to boost the convergence of implicit UGKS. Similar consideration can be found in Yuan et al [24].…”

Section: Two-step Iteration For Accelerationsupporting

confidence: 85%

General Implicit Iterative Method for Unified Gas-kinetic Scheme

Xu,

Zhu,

Liu

et al. 2021

Preprint

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In order to further enhance the computational efficiency of the implicit unified gas-kinetic scheme (IUGKS, JCP 315 (2016) for multi-scale flow simulation, a two-step IUGKS is proposed in this paper. The multiscale solution of the UGKS is determined by the integral solution of the kinetic model equation, which is composed of the Lagrangian integration of the equilibrium and the free particle transport of the nonequilibrium state. With the implicit evaluation of the macroscopic variables in the first iterative step, the integration of the equilibrium can be directly used in the flux calculation of macroscopic flow variables in the second iterative step. This is equivalent to include the viscous flux in the implicit scheme to accelerate the convergence of the solution instead of using the Euler flux in the iterative process of the original IUGKS. In the present IUGKS, the update of macroscopic flow variables are closely coupled with the implicit evolution of the gas distribution function. At the same time, in order to get the more accurate solution, the full Boltzmann collision term is incorporated into the current scheme through the penalty method. Different iterative techniques, such as LU-SGS and multi-grid, are used for solving the linear algebraic system of coupled macroscopic and microscopic equations. The efficiency of the IUGKS has reached a favorable level among all implicit schemes for the kinetic equations in the literature. Several numerical examples are used to validate the performance of the IUGKS. Accurate solutions have been obtained efficiently in all flow regimes from low speed to hypersonic ones.

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Section: Two-step Iteration For Accelerationsupporting

confidence: 85%

General Implicit Iterative Method for Unified Gas-kinetic Scheme

Xu,

Zhu,

Liu

et al. 2021

Preprint

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“…7 illustrates the contours of velocities, streamline and the velocity distribution along central horizontal and central vertical lines for Kn= 10 case. The results given by stochastic particle method with DR process almost overlap with those predicted by the deterministic UGKS method 58 . In the Kn= 0.075 case near continuum regime, the contours, streamline and distributions of macroscopic velocity also match well with the benchmark solution in Fig.…”

Section: Cavity Flowmentioning

confidence: 52%

A direct relaxation process for particle methods in gas kinetic theory

Yang,

Liu,

Zhong

et al. 2021

Preprint

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“…A similar idea of driving the convergence in the continuum regimes can be found in the development of the general synthetic iterative scheme (GSIS) [133,134]. From the study of Yuan et al [132], it can be found that the efficiency can be further improved by one order of magnitude on the basis of the original IUGKS for NS solutions in the continuum limit.…”

Section: Implicit Ugks and Multigrid Accelerationmentioning

confidence: 91%

“…This makes the IUGKS efficient in the low Knudsen number cases. In order to further improve the performance of the IUGKS for viscous flows, Yuan et al [132] took into account the NS terms during the macroscopic iterations. A similar idea of driving the convergence in the continuum regimes can be found in the development of the general synthetic iterative scheme (GSIS) [133,134].…”

Section: Implicit Ugks and Multigrid Accelerationmentioning

confidence: 99%

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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A multi-prediction implicit scheme for steady state solutions of gas flow in all flow regimes

Cited by 27 publications

References 39 publications

General Implicit Iterative Method for Unified Gas-kinetic Scheme

General Implicit Iterative Method for Unified Gas-kinetic Scheme

A direct relaxation process for particle methods in gas kinetic theory

GKS and UGKS for High-Speed Flows

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