Shear-driven micro/nano flows simulation using Fokker Planck approach: Investigating accuracy and efficiency

RezapourJaghargh, Vahid; Mahdavi, Amirmehran; Roohi, Ehsan

doi:10.1016/j.vacuum.2019.109065

Cited by 11 publications

(2 citation statements)

References 31 publications

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“…The Burgers equation [6,7], viscous and inviscid, is the simplest model, which shows the key feature for the whole gas dynamics: the existence of zones with strong gradients of the solution. Having correctly numerically simulated such zones, one can expect to build effective computational methods, not only and not so much for macro-models, but also for meso -levels of the hierarchy in the representation of the Kolmogorov -Fokker -Planck equations [1,8,9].…”

Section: Introductionmentioning

confidence: 99%

Visualization of the Application of the Discontinuous Particle Method without Taking into Account the Particle Shape to the Quasi-Linear Transport Equation

Богомолов¹,

Kuvshinnikov²

2021

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The paper considers a new variant of the discontinuous particle method. The main feature of the new variant is minimal smearing of discontinuities, due to the new criterion of rearrangement of particles. In contrast to the previously used variant with the analysis of overlaps of particles, which required an assumption about their shape, we use the key characteristic of particles, namely, their mass. The assumption is made that in nonlinear elastic transport not only the masses of the particles are conserved, but also the mass located between the centers of these particles. This requirement leads to the fact that a change of distance between particles in the process of their shear and conservation of mass in the space between them, lead to a change of density of one of the particles. The new version applies to solving the one-dimensional and two-dimensional quasi-linear transport equation problem. Visualization is used to monitor the numerical solution, showing that the shock velocity is calculated correctly, and the shock itself is smeared on one particle.

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Section: Introductionmentioning

confidence: 99%

Visualization of the Application of the Discontinuous Particle Method without Taking into Account the Particle Shape to the Quasi-Linear Transport Equation

Богомолов¹,

Kuvshinnikov²

2021

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“…70 Simulations of microscale rarefied flows were performed with the FP method, including the flows through a slit and an orifice, 71 the thermally induced gas flow in a ratchet microchannel, 72 and the shear-driven flows in microscale gaps and cavities. 73 Recently, Zhang and Önskog 74 utilized the FP molecular simulation to elucidate the mechanism of the macroscopic Rayleigh-Bénard instability from a microscopic point of view. Using the same approach, Zhang et al 75 numerically studied the instability and the transition to turbulence in the Kolmogorov flow, which provides evidence for capturing large-scale coherent structures through the simulation of molecular motions.…”

Section: Introductionmentioning

confidence: 99%

On the conservative property of particle-based Fokker–Planck method for rarefied gas flows

Jiang

Wen

2020

Physics of Fluids

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The Fokker-Planck-type approximation of the full Boltzmann equation has aroused intense research interest due to its potential for the stochastic particle simulation of rarefied gas flows. The ellipsoidal statistical Fokker-Planck (ES-FP) model treats the evolution of molecular velocity as a continuous stochastic process, and it satisfies the basic requirements for a proper gas-kinetic model including the H-theorem and an adjustable Prandtl number. The ES-FP model can be numerically implemented with computational particles in a Monte Carlo manner. Two different particle ES-FP schemes are presented. The first scheme utilizes the exact stochastic integral solution of the Langevin equations corresponding to the ES-FP equation and couples free-molecular moves and intermolecular collisions. The second scheme is designed to enforce the conservation of momentum and energy during the numerical simulation based on the decoupled algorithm and the analysis of the specific conditions for the conservative property. Numerical tests are conducted to demonstrate the performances of different schemes. In the simulation of a homogeneous gas system, the ES-FP scheme without enforcement of conservation leads to unphysical variation in the momentum and loss in energy, whereas the conservative ES-FP scheme strictly maintains the momentum and energy of the system. For the Mach 6 flows over the leading edge of a flat plate and over a round-nosed blunt body, the non-conservative ES-FP scheme underestimates the shock angle and the shock standoff distance, makes inaccurate predictions of aerodynamic force and heating, and produces low-temperature anomalies in front of the shock waves. In comparison with the results given by the direct simulation Monte Carlo method, the results of the conservative ES-FP simulations show satisfactory accuracy for the flow fields as well as the distributions of pressure, friction, and heat flux on the wall surfaces.

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A second-order particle Fokker-Planck model for rarefied gas flows

Kim,

Park,

Jun

2024

Computer Physics Communications

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Shear-driven micro/nano flows simulation using Fokker Planck approach: Investigating accuracy and efficiency

Cited by 11 publications

References 31 publications

Visualization of the Application of the Discontinuous Particle Method without Taking into Account the Particle Shape to the Quasi-Linear Transport Equation

Visualization of the Application of the Discontinuous Particle Method without Taking into Account the Particle Shape to the Quasi-Linear Transport Equation

On the conservative property of particle-based Fokker–Planck method for rarefied gas flows

A second-order particle Fokker-Planck model for rarefied gas flows

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