Lattice Boltzmann approach to rarefied gas flows using half-range Gauss-Hermite quadratures: Comparison to DSMC results based on ab initio potentials

Ambruş, Victor E.; Sharipov, Felix; Sofonea, Victor

doi:10.1063/1.5119552

Cited by 6 publications

(6 citation statements)

References 26 publications

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“…More complex flows, where the application of half-range Gauss-Hermite quadrature is essential are investigated in Refs. [50,54,55].…”

Section: Simulation Resultsmentioning

confidence: 99%

“…Finally, more complex relaxation time models, such as the Shakhov model [74,75], can be implemented as described in, e.g., Refs. [54,55].…”

Section: Discussionmentioning

confidence: 99%

“…In this chapter, we follow Refs. [50,54,55] and perform an equidistant grid discretisation with respect to the non-dimensional parameter η, defined through:…”

Section: Couette Flow Between Parallel Platesmentioning

confidence: 99%

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Quadrature-Based Lattice Boltzmann Models for Rarefied Gas Flow

Ambruş

Sofonea

2019

Soft and Biological Matter

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At non-negligible values of the Knudsen number Kn (defined as the ratio between the mean free path of the fluid particles in a gas and the characteristic length of the domain), the Navier-Stokes equations lose applicability [1, 2]. Such rarefied gas flows can be approached within the framework of the Boltzmann equation [3-5]. This equation describes the six-dimensional phase-space evolution of the distribution function f , where f (t, x, p)d 3 xd 3 p gives the number of particles at time t which are contained in an infinitesimal volume d 3 x centred on x, having momenta in an infinitesimal range d 3 p about p. Because of its complexity, the Boltzmann equation can be solved analytically only in a very limited number of cases. Alternatively, numerous well-established approaches to the numerical solutions of the Boltzmann equation are now currently used for academic or engineering purposes, of which we only mention the direct simulation Monte Carlo (DSMC) technique [6], the discrete velocity models (DVMs) [7-9], the discrete unified gas-kinetic scheme (DUGKS) [10-12] and the lattice Boltzmann (LB) models [13-20]. The LB models are a particular type of DVMs and are derived from the Boltzmann equation using a simplified version of the collision operator, as well as an appropriate discretisation of the momentum space, which ensure the recovery of the moments of the distribution function f up to a certain order N. Originally derived nearly 30 years ago from the lattice gas automata [17, 19, 20], the LB

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“…More complex flows, where the application of half-range Gauss-Hermite quadrature is essential are investigated in Refs. [50,54,55].…”

Section: Simulation Resultsmentioning

confidence: 99%

“…Finally, more complex relaxation time models, such as the Shakhov model [74,75], can be implemented as described in, e.g., Refs. [54,55].…”

Section: Discussionmentioning

confidence: 99%

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Quadrature-Based Lattice Boltzmann Models for Rarefied Gas Flow

Ambruş

Sofonea

2019

Soft and Biological Matter

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“…To overcome these shortcomings, a variety of Boltzmann equation-based mesoscopic methods have been developed and applied in recent years to study rarefied gas flows [39,40]. These include discrete velocity method (DVM) [41][42][43], the gas kinetic scheme (GKS) [42,44,45], the lattice Boltzmann (LB) method [46][47][48][49][50][51], and R13 equations which are derived as approximations of the Boltzmann that is combination of the Chapman-Enskog and Grad methods [52,53]. LB method is beneficial for applications where microscopic details are not required and hence, the computationally expensive methods such as DSMC and direct numerical simulation of the Boltzmann equation can be avoided [54].…”

Section: Mamentioning

confidence: 99%

A review of rarefied gas flow in irregular micro/nanochannels

Taassob

Bordbar

Kheirandish

et al. 2021

J. Micromech. Microeng.

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In today’s complex micro–electro–mechanical systems (MEMS), investigation of flow through irregular micro/nanochannels, such as bended channels, variable cross-sectional area channels, and those with rough surfaces, can contribute considerably to efficient designing of the microdevices and to gain a better understanding of the flow structure in these geometries. The present paper reviews the prominent studies published in literature on rarefied gas flow through these types of complex geometries. The main focus of the study is to explore the physical aspects of the findings and the analyses provided in support of the results. Finally, the areas in which a gap exists in literature and could be subjects of future studies are introduced.

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“…This can be achieved by performing a coordinate change from x = x/ L to the coordinate η, defined through [25,75,77,81]:…”

Section: Time Stepping and Advectionmentioning

confidence: 99%

Comparison of the Shakhov and ellipsoidal models for the Boltzmann equation and DSMC for ab initio-based particle interactions

Ambrus,

Sharipov,

Sofonea

2019

Preprint

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In this paper, we consider the capabilities of the Boltzmann equation with the Shakhov or ellipsoidal models for the collision term to capture the characteristics of rarefied gas flows. The benchmark is performed by comparing the results obtained using these kinetic model equations with direct simulation Monte Carlo (DSMC) results for particles interacting via ab initio potentials. The analysis is restricted to channel flows between parallel plates and we consider three flow problems, namely: the heat transfer between stationary plates, the Couette flow and the heat transfer under shear. The simulations are performed in the nonlinear regime for the 3 He, 4 He, and Ne gases. The reference temperature ranges between 1 K and 3000 K for 3 He and 4 He and between 20 K and 5000 K for Ne. While good agreement is seen up to the transition regime for the direct phenomena (shear stress, heat flux driven by temperature gradient), the relative errors in the cross phenomena (heat flux perpendicular to the temperature gradient) exceed 10% even in the slip-flow regime. The kinetic model equations are solved using the finite difference lattice Boltzmann algorithm based on half-

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Lattice Boltzmann approach to rarefied gas flows using half-range Gauss-Hermite quadratures: Comparison to DSMC results based on ab initio potentials

Cited by 6 publications

References 26 publications

Quadrature-Based Lattice Boltzmann Models for Rarefied Gas Flow

Quadrature-Based Lattice Boltzmann Models for Rarefied Gas Flow

A review of rarefied gas flow in irregular micro/nanochannels

Comparison of the Shakhov and ellipsoidal models for the Boltzmann equation and DSMC for ab initio-based particle interactions

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