A unified stochastic particle Bhatnagar-Gross-Krook method for multiscale gas flows

Fei, Fei; Zhang, Jun; Li, Jing; Liu, Zhaohui

doi:10.1016/j.jcp.2019.108972

Cited by 57 publications

(45 citation statements)

References 51 publications

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“…This limits the application of the particle BGK method to continuum flows. To reduce the numerical dissipation of the ESBGK and SBGK method, and obtain an asymptotic-preserving property in the NS limit, a Unified Stochastic Particle-BGK (USP-BGK) method [15] has been developed recently. In the USP-BGK method, the BGK equation is rewritten as Fig.…”

Section: Unified Stochastic Particle Bgk Methodsmentioning

confidence: 99%

“…Compared to the UGKS and DUGKS methods, particle-particle hybrid methods are more efficient for the simulation of high-speed gas flows, especially when complex physical and chemical effects are considered. The latest progress in this direction is the unified particle method by combining the particle convection and collision effects [15]. The advantage is that it can be used with large time steps for the continuum flow, and thus the computational efficiency is highly improved.…”

Section: Introductionmentioning

confidence: 99%

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Particle-based hybrid and multiscale methods for nonequilibrium gas flows

et al. 2019

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Over the past half century, a variety of computational fluid dynamics (CFD) methods and the direct simulation Monte Carlo (DSMC) method have been widely and successfully applied to the simulation of gas flows for the continuum and rarefied regime, respectively. However, they both encounter difficulties when dealing with multiscale gas flows in modern engineering problems, where the whole system is on the macroscopic scale but the nonequilibrium effects play an important role. In this paper, we review two particle-based strategies developed for the simulation of multiscale nonequilibrium gas flows, i.e., DSMC-CFD hybrid methods and multiscale particle methods. The principles, advantages, disadvantages, and applications for each method are described. The latest progress in the modelling of multiscale gas flows including the unified multiscale particle method proposed by the authors is presented.

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Section: Unified Stochastic Particle Bgk Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Particle-based hybrid and multiscale methods for nonequilibrium gas flows

et al. 2019

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“…In order to extend DSMC to the continuum flow simulation, the asymptotic preserving Monte Carlo methods [7,8], moment-guided Monte Carlo method [9], low diffusion particle method [10], as well as hybrid methods between DSMC and CFD methods [11] have been constructed. The stochastic methods based on the kinetic model equations, for example the BGK/ES-BGK equation [12,13] and the kinetic Fokker-Planck equation [14] have been proposed to reduce the computational cost of DSMC. Among those stochastic kinetic methods, the particle Fokker-Planck method [14] and the stochastic BGK method [13] are applicable over different flow regimes.…”

Section: Introductionmentioning

confidence: 99%

“…The stochastic methods based on the kinetic model equations, for example the BGK/ES-BGK equation [12,13] and the kinetic Fokker-Planck equation [14] have been proposed to reduce the computational cost of DSMC. Among those stochastic kinetic methods, the particle Fokker-Planck method [14] and the stochastic BGK method [13] are applicable over different flow regimes. The deterministic discrete ordinate methods (DOM) for Boltzmann and kinetic equations have been extensively studied in the last several decades [15][16][17][18][19][20][21][22][23], which have great advantages for the simulation of low speed microflow [24,25].…”

Section: Introductionmentioning

confidence: 99%

Unified gas-kinetic wave-particle methods I: Continuum and rarefied gas flow

Liu

Zhu

2020

Journal of Computational Physics

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The unified gas-kinetic scheme (UGKS) provides a framework for simulating multiscale transport with the updates of both gas distribution function and macroscopic flow variables on the cell size and time step scales. The multiscale dynamics in UGKS is achieved through the coupled particle transport and collision in the particle evolution process within a time step. In this paper, under the UGKS framework, we propose an efficient multiscale unified gas-kinetic wave-particle (UGKWP) method. The gas dynamics in UGKWP method is described by the individual particle movement coupled with the evolution of the probability density function (PDF). During a time step, the trajectories of simulation particles are tracked until collision happens, and the post-collision particles are evolved collectively through the evolution of the corresponding distribution function. The evolution of simulation particles and distribution function is guided by evolution of macroscopic variables. The two descriptions on a gas particle, i.e. wave and particle, switch dynamically with time. A new concept of multiscale multi-efficiency preserving (MMP) method is introduced, and the UGKWP method is shown to be an MMP scheme. Multiscale preserving means UGKWP method preserves the flow regime from collisionless regime to hydrodynamic regime without requiring the cell size and time step to be less than the mean free path and collision time. Multi-efficiency preserving means the computational cost of UGKWP method including the computational time and memory cost is on the same level as the particle methods in the rarefied regime, and becomes comparable to the hydrodynamic solvers in continuum regime. The UGKWP method is specially efficient for hypersonic flow simulation in all regimes in comparison with the wave-type discrete ordinate 1 arXiv:1811.07141v1 [math.NA] 17 Nov 2018 methods, and presents a much lower stochastic noise in the continuum flow regime in comparison with the particle-based Monte Carlo methods. Numerical tests for flows over a wide range of Mach and Knudsen numbers are presented. The examples include mainly the hypersonic flow passing a circular cylinder at Mach numbers 20 and 30 and Knudsen numbers 1 and 10 −4 , low speed lid-driven cavity flow, and laminar boundary layer. These results validate the accuracy, efficiency, and multiscale property of UGKWP method.

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“…For the last several decades, researchers has been trying to develop effective multiscale numerical schemes [4][5][6][7][8][9]. In 2010, Xu et al proposes the unified gas-kinetic scheme, which is the first genuine multiscale scheme being able to capture the viscous effect with cell size much larger than the kinetic scale.…”

Section: Introductionmentioning

confidence: 99%

A Unified Gas-kinetic Scheme for Micro Flow Simulation Based on Linearized Kinetic Equation

Liu

2020

Preprint

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The flow regime of micro flow varies from collisionless regime to hydrodynamic regime according to the Knudsen number. On the kinetic scale, the dynamics of micro flow can be described by the linearized kinetic equation. In the continuum regime, hydrodynamic equations such as linearized Navier-Stokes equations and Euler equations can be derived from the linearized kinetic equation by the Chapman-Enskog asymptotic analysis. In this paper, based on the linearized kinetic equation we are going to propose a unified gas kinetic scheme scheme (UGKS) for micro flow simulation, which is an effective multiscale scheme in the whole micro flow regime. The important methodology of UGKS is the following. Firstly, the evolution of microscopic distribution function is coupled with the evolution of macroscopic flow quantities. Secondly, the numerical flux of UGKS is constructed based on the integral solution of kinetic equation, which provides a genuinely multiscale and multidimensional numerical flux. The UGKS recovers the linear kinetic solution in the rarefied regime, and converges to the linear hydrodynamic solution in the continuum regime. An outstanding feature of UGKS is its capability of capturing the accurate viscous solution even when the cell size is much larger than the kinetic kinetic length scale, such as the capturing of the viscous boundary layer with a cell size ten times larger than the particle mean free path. Such a multiscale property is called unified preserving (UP) which has been studied in \cite{guo2019unified}. In this paper, we are also going to give a mathematical proof for the UP property of UGKS.

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A unified stochastic particle Bhatnagar-Gross-Krook method for multiscale gas flows

Cited by 57 publications

References 51 publications

Particle-based hybrid and multiscale methods for nonequilibrium gas flows

Particle-based hybrid and multiscale methods for nonequilibrium gas flows

Unified gas-kinetic wave-particle methods I: Continuum and rarefied gas flow

A Unified Gas-kinetic Scheme for Micro Flow Simulation Based on Linearized Kinetic Equation

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