Fokker–Planck–DSMC algorithm for simulations of rarefied gas flows

Gorji, M. Hossein; Jenny, Patrick

doi:10.1016/j.jcp.2015.01.041

Cited by 70 publications

(32 citation statements)

References 28 publications

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“…Alternatively, some researchers have made efforts to develop a particle-particle hybrid method, such as BGK-DSMC [16][17][18][19] and Fokker-Planck-DSMC [20][21][22][23] methods, where the particle simulation methods based on BGK or Fokker-Planck model are employed for the continuum regime, while DSMC method is used for the rarefied regime. It is known that BGK [24,25] or Fokker-Planck [26] model simplifies the collision term in the Boltzmann equation, so their corresponding particle methods can achieve much higher efficiency than DSMC in the continuum regime.…”

Section: Introductionmentioning

confidence: 99%

“…Note that three different time steps and cell sizes are used for each case, and , cl  represents the initial mean collision time for the left chamber. To investigate the unsteady process, both cases are simulated up to the time steady flows, a large number of particles are employed here to reduce statistical noise.Similar to the Fokker-Planck-DSMC method employed in ref [20],. computational particles are initially arranged in one computational cell in the right and left chambers, respectively.…”

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confidence: 99%

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

Fei

Zhang

et al. 2020

Journal of Computational Physics

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The stochastic particle method based on Bhatnagar-Gross-Krook (BGK) or ellipsoidal statistical BGK (ESBGK) model approximates the pairwise collisions in the Boltzmann equation using a relaxation process.Therefore, it is more efficient to simulate gas flows at small Knudsen numbers than the counterparts based on the original Boltzmann equation, such as the Direct Simulation Monte Carlo (DSMC) method. However, the traditional stochastic particle BGK method decouples the molecular motions and collisions in analogy to the DSMC method, and hence its transport properties deviate from physical values as the time step increases. This defect significantly affects its computational accuracy and efficiency for the simulation of multiscale flows, especially when the transport processes in the continuum regime is important. In the present paper, we propose a unified stochastic particle ESBGK (USP-ESBGK) method by combining the molecular convection and collision effects. In the continuum regime, the proposed method can be applied using large temporal-spatial discretization and approaches to the Navier-Stokes solutions accurately. Furthermore, it is capable to simulate both the small scale non-equilibrium flows and large scale continuum flows within a unified framework efficiently and accurately. The applications of USP-ESBGK method to a variety of benchmark problems, including Couette flow, thermal Couette flow, Poiseuille flow, Sod tube flow, cavity flow, and flow through a slit, demonstrated that it is a promising tool to simulate multiscale gas flows ranging from rarefied to continuum regime.

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Section: Introductionmentioning

confidence: 99%

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confidence: 99%

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

Fei

Zhang

et al. 2020

Journal of Computational Physics

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“…The Fokker-Planck (FP) equation with advection-diffusion collision operator is widely used in modeling dynamic systems such as neutral molecule [1,2,3], plasma [4,5,6], photonics [7,8], and even biological [9], economic [10], and social [11] systems. The first FP equation for molecule system is derived from Boltzmann equation in gas kinetic theory when counting the gazing effect of molecule collisions [12].…”

Section: Introductionmentioning

confidence: 99%

“…They are cubic-FP equation [2] and ellipsoidal-FP (ES-FP) equation [3]. Recently, by mapping these FP equations to Stochastic Differential Equations (SDEs), the FP equations are solved in a stochastic and particle way [1,2]. Comparing with other particle methods such as Direct Simulation Monte-Carlo (DSMC) [13], its computational cost is greatly reduced in continuum limit (dissipation limit in FP research).…”

Section: Introductionmentioning

confidence: 99%

Conservative discrete-velocity method for the ellipsoidal Fokker-Planck equation in gas-kinetic theory

et al. 2019

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A conservative discrete velocity method (DVM) is developed for the ellipsoidal Fokker-Planck (ES-FP) equation in prediction of non-equilibrium neutral gas flows in this paper. The ES-FP collision operator is solved in discrete velocity space in a concise and quick finite difference framework. The conservation problem of discrete ES-FP collision operator is solved by multiplying each term in it by extra conservative coefficients whose values are very closed to unity. Their differences to unity are in the same order of the numerical error in approximating the ES-FP operator in discrete velocity space. All the macroscopic conservative variables (mass, momentum and energy) are conserved in the present modified discrete ES-FP collision operator. Since the conservation property in discrete element of physical space is very important for numerical scheme when discontinuity and large gradient exist in flow field, a finite volume framework is adopted for the transport term of ES-FP equation. For nD-3V (n < 3) cases, a nD-quasi nV reduction is specially proposed for ES-FP equation and the corresponding FP-DVM method, which can greatly reduce the computational cost. The validity and accuracy of both ES-FP equation and FP-DVM method are examined using a series of 0D-3V homogenous relaxation cases and 1D-3V shock structure cases with different M ach numbers, in which 1D-3V cases are reduced to 1D-quasi 1V cases. Both the predictions of 0D-3V and 1D-3V cases match well with the benchmark results such as analytical Boltzmann solution, direct full-Boltzmann numerical solution and DSMC result. Especially, the FP-DVM predictions match well with the DSMC results in the M ach 8.0 shock structure case, which is in high non-equilibrium, and is a challenge case of the model Boltzmann equation and the corresponding numerical methods.

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“…That models are often called Kolmogorov -Fokker -Planck equations. They are used by theoreticians [2] and applied mathematicians [3,4]. The last ones mostly implement the models of so-called maxwellian molecules, not hard sphere ones, that lead to considerably different results [5].…”

Section: Introductionmentioning

confidence: 99%

Meso - Macro Models for a Hard Sphere Gas

Богомолов¹,

Esikova²,

Kuvshinnikov³

2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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Abstract. Macroscopic system of gas dynamic equations, differing from Navier -Stokes and quasi gas dynamic ones, is derived from a stochastic microscopic model of a hard sphere gas in a phase space. The model is diffusive in velocity space and valid for moderate Knudsen numbers. The main peculiarity of our derivation is more accurate velocity averaging due to analytical solving stochastic differential equations with respect to Wiener measure which describe our original meso model. It is shown at an example of a shock wave front structure that our approach leads to larger than Navier -Stokes front widening that corresponds to reality. The numerical solution is performed by a (well suited to high performance computer applications) special "discontinuous" particle method.3121

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Fokker–Planck–DSMC algorithm for simulations of rarefied gas flows

Cited by 70 publications

References 28 publications

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

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

Conservative discrete-velocity method for the ellipsoidal Fokker-Planck equation in gas-kinetic theory

Meso - Macro Models for a Hard Sphere Gas

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