Frequency-domain Monte Carlo method for linear oscillatory gas flows

Ladiges, Daniel R.; Sader, John E.

doi:10.1016/j.jcp.2014.12.036

Cited by 10 publications

(3 citation statements)

References 42 publications

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“…2. Since the limitation on the cell size is removed and fast convergence is enabled, the present synthetic iteration scheme can be directly applied to low-variance [60,61] and even frequency-domain [62] DSMC that solves the linearized Boltzmann/kinetic model equations to improve the computational efficiency, especially in the near-continuum flow regime. 3.…”

Section: Conclusion and Outlooksmentioning

confidence: 99%

Can we find steady-state solutions to multiscale rarefied gas flows within dozens of iterations?

Zhu

Wang

et al. 2020

Journal of Computational Physics

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One of the central problems in the study of rarefied gas dynamics is to find the steady-state solution of the Boltzmann equation quickly. When the Knudsen number is large, i.e. the system is highly rarefied, the conventional iteration scheme can lead to convergence within a few iterations. However, when the Knudsen number is small, i.e. the flow falls in the nearcontinuum regime, hundreds of thousands iterations are needed, and yet the "converged" solutions are prone to be contaminated by accumulated error and large numerical dissipation. Recently, based on the gas kinetic models, the implicit unified gas kinetic scheme (UGKS) and its variants have significantly reduced the iterations in the near-continuum flow regime, but still much higher than that of the highly rarefied gas flows. In this paper, we put forward a general synthetic iteration scheme (GSIS) to find the steady-state solutions of general rarefied gas flows within dozens of iterations at any Knudsen number. The key ingredient of our scheme is that the macroscopic equations, which are solved together with the Boltzmann equation and help to adjust the velocity distribution function, not only asymptotically preserves the Navier-Stokes limit in the framework of Chapman-Enskog expansion, but also contain Newton's law for stress and Fourier's law for heat conduction explicitly. For this reason, like implicit UGKS, the constraint that the numerical cell size should be smaller than the mean free path of gas molecules is removed, but we do not need the complex evaluation of numerical flux at the cell interface. What's more, as the GSIS does not rely on the specific kinetic model/collision operator, it can be naturally extended to quickly find converged solutions for mixture flows and even flows involving chemical reactions. These two superior advantages are also expected to accelerate the slow convergence in simulation of near-continuum flows via the direct simulation Monte Carlo method and its low-variance version. * Wei Su and Lianhua Zhu contribute equally.

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Section: Conclusion and Outlooksmentioning

confidence: 99%

Can we find steady-state solutions to multiscale rarefied gas flows within dozens of iterations?

Zhu

Wang

et al. 2020

Journal of Computational Physics

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“…No-slip boundaries were implemented on the solid surfaces. The second approach includes the effects of gas rarefaction by simulating the system using the frequency-domain Monte Carlo Method. , This approach solves the Boltzmann Transport Equation (BTE), and should therefore provide more accurate results for low gas pressures. The simulations are benchmarked against a previously published data set from a 5 μm diameter drum from 31-layer graphene over a 400 nm deep cavity, which is shown in the Supporting Information section S3.…”

mentioning

confidence: 99%

“…The second approach includes the effects of gas rarefaction by simulating the system using the frequency-domain Monte Carlo Method. 39,40 This approach solves the Boltzmann Transport Equation (BTE), and should therefore provide more accurate results for low gas pressures.…”

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confidence: 99%

Squeeze-Film Effect on Atomically Thin Resonators in the High-Pressure Limit

et al. 2021

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The resonance frequency of membranes depends on the gas pressure due to the squeeze-film effect, induced by the compression of a thin gas film that is trapped underneath the resonator by the high-frequency motion. This effect is particularly large in low-mass graphene membranes, which makes them promising candidates for pressure-sensing applications. Here, we study the squeeze-film effect in single-layer graphene resonators and find that their resonance frequency is lower than expected from models assuming ideal compression. To understand this deviation, we perform Boltzmann and continuum finite-element simulations and propose an improved model that includes the effects of gas leakage and can account for the observed pressure dependence of the resonance frequency. Thus, this work provides further understanding of the squeeze-film effect and provides further directions into optimizing the design of squeeze-film pressure sensors from 2D materials.

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