Variance-reduced DSMC for binary gas flows as defined by the McCormack kinetic model

Szalmás, Lajos

doi:10.1016/j.jcp.2012.01.016

Cited by 19 publications

(12 citation statements)

References 23 publications

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“…McCormack kinetic equation for binary gas mixtures [17]. Excellent agreement with other deterministic solvers has been reported.…”

Section: And Thementioning

confidence: 64%

A comparative study of the DSBGK and DVM methods for low-speed rarefied gas flows

et al. 2019

Computers & Fluids

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Low-speed rarefied gas flow in a lid-driven cavity is chosen as a test case in order to assess the accuracy and efficiency of both the Direct Simulation Bhatnagar-Gross-Krook (DSBGK) method and the Discrete Velocity Method (DVM) for solving the BGK kinetic equation. Various lid-speeds and a broad range of rarefaction levels, from slip to near free-molecular flows, are investigated. The DSBGK and DVM results are in satisfactory agreement for all the examined cases in 2D and 3D. As a statistical method, the stochastic noise of the DSBGK method is much smaller than that of the conventional Direct Simulation Monte Carlo (DSMC) method, and is independent of the Mach number. To achieve the required accuracy, the DSBGK simulations need more CPU time than the DVM simulations, i.e. for the 2D cases, a factor of 2 to 15 times more for convergence, and about 50 to 80 times more overall, including the time-averaging process. However, for 3D cases, the third direction in the DVM velocity grid is needed, so the computational cost of DSBGK is now only 0.16 to 0.51 times that of the DVM for the convergence process, and 1.6 to 5.8 times that of the DVM overall. The efficiency of the DSBGK method can also be expected to be enhanced in large-scale 3D simulations, where the computational cost for time-averaging becomes negligible in comparison with the convergence process. The DSBGK simulations require much less memory, even at low Mach numbers, than the DVM simulations; in the test cases with the required accuracy, about 10 simulated molecules per cell in the DSBGK simulations are sufficient for an arbitrary

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“…McCormack kinetic equation for binary gas mixtures [17]. Excellent agreement with other deterministic solvers has been reported.…”

Section: And Thementioning

confidence: 64%

A comparative study of the DSBGK and DVM methods for low-speed rarefied gas flows

et al. 2019

Computers & Fluids

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“…Recently, some improvements have been made to ease the difficulties [7][8][9][10] . It is noted that the deterministic Boltzmann solvers can also be applied to gas mixture flows in simple geometries by direct discretizing the full Boltzmann equation [11][12][13][14][15] .…”

Section: Introductionmentioning

confidence: 99%

Discrete unified gas kinetic scheme for flows of binary gas mixture based on the McCormack model

2019

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The discrete unified gas kinetic scheme (DUGKS) was originally developed for singlespecies flows covering all the regimes, while the gas mixtures are more frequently encountered in engineering applications. Recently, the DUGKS has been extended to binary gas mixtures of Maxwell molecules on the basis of the Andries-Aoki-Perthame kinetic model (AAP) [P. Andries et al., J. Stat. Phys. 106, 993 (2002)]. However, the AAP model cannot recover a correct Prandtl number. In this work, we extend the DUGKS to gas mixture flows based on the McCormack model [F. J. McCormack, Phys. Fluids 16, 2095 (1973)], which can give all the transport coefficients correctly. The proposed method is validated by several standard tests, including the plane Couette flow, the Fourier flow, and the lid-driven cavity flow under different mass ratios and molar concentrations. Good agreement between results of the DUGKS and the other well-established numerical methods shows that the proposed DUGKS is effective and reliable for binary gas mixtures in all flow regimes. In addition, the DUGKS is about two orders of magnitude faster than the DSMC for low-speed flows in terms of the wall time and convergent iteration steps.

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“…This limitation leads to expensive computational costs for continuum and near-continuum flows. It is noted that some efforts have been made to reduce these difficulties [7,8]. Besides the DSMC method, some deterministic numerical methods for the Boltzmann equation, such as [9][10][11][12], have been applied to gas mixtures flows with simple geometries.…”

Section: Introductionmentioning

confidence: 99%

Discrete unified gas kinetic scheme for all Knudsen number flows. III. Binary gas mixtures of Maxwell molecules

2018

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Recently a discrete unified gas kinetic scheme (DUGKS) in a finite-volume formulation based on the Boltzmann model equation has been developed for gas flows in all flow regimes. The original DUGKS is designed for flows of single-species gases. In this work, we extend the DUGKS to flows of binary gas mixtures of Maxwell molecules based on the Andries-Aoki-Perthame kinetic model [P. Andries et al., J. Stat. Phys. 106, 993 (2002)JSTPBS0022-471510.1023/A:1014033703134. A particular feature of the method is that the flux at each cell interface is evaluated based on the characteristic solution of the kinetic equation itself; thus the numerical dissipation is low in comparison with that using direct reconstruction. Furthermore, the implicit treatment of the collision term enables the time step to be free from the restriction of the relaxation time. Unlike the DUGKS for single-species flows, a nonlinear system must be solved to determine the interaction parameters appearing in the equilibrium distribution function, which can be obtained analytically for Maxwell molecules. Several tests are performed to validate the scheme, including the shock structure problem under different Mach numbers and molar concentrations, the channel flow driven by a small gradient of pressure, temperature, or concentration, the plane Couette flow, and the shear driven cavity flow under different mass ratios and molar concentrations. The results are compared with those from other reliable numerical methods. The results show that the proposed scheme is an effective and reliable method for binary gas mixtures in all flow regimes.

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Variance-reduced DSMC for binary gas flows as defined by the McCormack kinetic model

Cited by 19 publications

References 23 publications

A comparative study of the DSBGK and DVM methods for low-speed rarefied gas flows

A comparative study of the DSBGK and DVM methods for low-speed rarefied gas flows

Discrete unified gas kinetic scheme for flows of binary gas mixture based on the McCormack model

Discrete unified gas kinetic scheme for all Knudsen number flows. III. Binary gas mixtures of Maxwell molecules

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