Application of the integro-moment method to steady-state two-dimensional rarefied gas flows subject to boundary induced discontinuities

Varoutis, S.; Valougeorgis, Dimitris; Sharipov, Felix

doi:10.1016/j.jcp.2008.03.008

Cited by 25 publications

(21 citation statements)

References 27 publications

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“…where ξ is the molecular speed and s is the coordinate along the characteristic line [28]. Choosing ξ to be the most probable speed, Eq.…”

Section: A the Average Gas Pressurementioning

confidence: 99%

Sound propagation through a rarefied gas in rectangular channels

2016

Phys. Rev. E

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This version is available at https://strathprints.strath.ac.uk/58309/ Strathprints is designed to allow users to access the research output of the University of Strathclyde. Unless otherwise explicitly stated on the manuscript, Copyright © and Moral Rights for the papers on this site are retained by the individual authors and/or other copyright owners. Please check the manuscript for details of any other licences that may have been applied. You may not engage in further distribution of the material for any profitmaking activities or any commercial gain. You may freely distribute both the url (https://strathprints.strath.ac.uk/) and the content of this paper for research or private study, educational, or not-for-profit purposes without prior permission or charge.Any correspondence concerning this service should be sent to the Strathprints administrator: strathprints@strath.ac.ukThe Strathprints institutional repository (https://strathprints.strath.ac.uk) is a digital archive of University of Strathclyde research outputs. It has been developed to disseminate open access research outputs, expose data about those outputs, and enable the management and persistent access to Strathclyde's intellectual output.Sound propagation through a rarefied gas in rectangular channels A sound propagation through a rarefied gas inside a two-dimensional cavity is investigated on the basis of the linearized Boltzmann equation, where one of the cavity wall oscillates harmonically in the normal direction to its own surface and is considered as a sound source. An analytical solution at high oscillation frequencies is obtained, and detailed numerical results for a wide range of gas rarefaction are presented. The influence of both the aspect ratio of the cavity and the oscillation frequency on the average gas pressure exerted on the oscillating plate is studied. It is found that, at large values of the aspect ratio, the average pressure oscillates when the sound frequency varies, due to the sound resonance and anti-resonance along the oscillation direction of the plate. However, at small values of the aspect ratio, the average pressure is a monotonically decreasing function of the sound frequency, which cannot be observed in the corresponding one-dimensional counterpart. This is explained by the sound interference in the direction parallel to the oscillating plate. The influence of both the cavity aspect ratio and oscillation frequency on the sound speed is also investigated: again it is found that different aspect ratio leads to the different behavior of the sound speed as a function of the oscillation frequency.

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“…where ξ is the molecular speed and s is the coordinate along the characteristic line [28]. Choosing ξ to be the most probable speed, Eq.…”

Section: A the Average Gas Pressurementioning

confidence: 99%

Sound propagation through a rarefied gas in rectangular channels

2016

Phys. Rev. E

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“…In fact, in order to update h n i,j the values of the distribution function of two upwind neighboring nodes, often referred to as "halo" nodes [16], are required. The halos on one physical direction can be read in with coalesced access (line [13][14][15][16][17][18][19] while the others have to be read in with non-coalesced access (line [6][7][8][9][10][11][12]. Threads which update boundary points perform calculations which are slightly different to account for the incoming Maxwellian flux from the boundaries of the domain (lines 8 and 15).…”

Section: Cuda Tm Implementationmentioning

confidence: 99%

“…Afterwards, the post-collisional velocities are evaluated (line 4-6) and the index of the velocity cells to which they belong are calculated and stored in the vectors I, I 1 , I * and I * 1 defined in the global memory (lines 7-10). Finally, for each velocity cell, the values to be added and subtracted to these velocity cells are calculated (lines [11][12][13][14] and stored (lines [15][16][17][18] in the vectors C, C 1 , C * and C * 1 defined in the global memory. It is important to note that in order to maximize the performance all the accesses to the global memory are done in a coalesced manner [15].…”

Section: Cuda Tm Implementationmentioning

confidence: 99%

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Solving the Boltzmann equation on GPUs

Frezzotti

Ghiroldi

Gibelli

2011

Computer Physics Communications

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We show how to accelerate the direct solution of the Boltzmann equation using Graphics Processing Units (GPUs). In order to fully exploit the computational power of the GPU, we choose a method of solution which combines a finite difference discretization of the free-streaming term with a Monte Carlo evaluation of the collision integral. The efficiency of the code is demonstrated by solving the two-dimensional driven cavity flow. Computational results show that it is possible to cut down the computing time of the sequential code of two order of magnitude. This makes the proposed method of solution a viable alternative to particle simulations for studying unsteady low Mach number flows

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“…Boltzmann method [88,89], the Information Preservation method [90,51], the Analytical Discrete Ordinate method [91,92], moment methods [93,94], variational methods [95], extended hydrodynamic equation systems [48] etc. Even though these methods can also be very effective, limitations related to applicability range, generality, accuracy or complexity usually lead us to the selection of DVM or DSMC.…”

Section: Methodsmentioning

confidence: 99%

Simulation of transport phenomena in conditions far from thermodynamic equilibrium via kinetic theory with applications in vacuum technology and MEMS

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The approval of the current dissertation by the Department of Mechanical Engineering of the University of Thessaly does not imply acceptance of the author's opinions (Law 5343/32 number 202 paragraph 2). Also, the views and opinions expressed herein do not necessarily reflect those of the European Commission. There are several other people who I feel that have contributed in the writing of this dissertation.The most important contributions, along with several helpful conversations, were made by Prof. F.Sharipov, who provided the basic concept of the channel end effect study, and Dr. Chr. Day along with the KIT personnel, who briefly introduced me in the world of experimental rarefied gas dynamics. It was also a priviledge to discuss and work for a brief period of time with Prof. A. Grecos, who tirelessly discussed with me on various subjects of statistical mechanics. Financial support for this Ph.D. has been provided by the Euratom Association -Hellenic Republic, to which I am deeply indepted. Also, partial support for conference mobility expenses has been received from the GASMEMS Marie Curie programme. In this work, non-equilibrium transport phenomena have been examined via the kinetic theory of gases. The behaviour of the gas in low pressure conditions or in low-dimensionality systems can not be captured by the usual Navier-Stokes formulation, in conjunction with the constitutive laws of Newton-Fourier-Fick. The limited number of intermolecular collisions results in departure from equilibrium and the particulate nature of the gas must be taken into account, greatly increasing the computational effort.The problem is described by the integro-differential Boltzmann equation, which is used to determine the distribution of particles in physical and molecular velocity space, as well as in time.There are difficulties associated with the seven-dimensional nature of the distribution function, as well as with the complexity of the collision term, which is usually substituted by an appropriate model.The most widely used and successful numerical methodologies, the Discrete Velocity Method (DVM) and the Direct Simulation Monte Carlo (DSMC), are applied here in the whole range of the Knudsen number. It is important to employ approaches based on kinetic theory, since these are the only ones which are valid for any rarefaction level.In this work, several problems including non-equilibrium phenomena are considered. The interaction of gases with solid surfaces is considered for several problems according to the CercignaniLampis boundary conditions. The non-linear form of this scattering kernel, which had not been pre- viously used in the literature, is applied on the problem of heat transfer between parallel plates and coaxial cylinders. Its linearized form has also been employed for both flow and heat transfer problems and a comparison with relevant experiments has lead to surface characterization with respect to argon and helium flows.Non-linear heat conduction phenomena are also studied for the parallel plates and coaxial c...

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Application of the integro-moment method to steady-state two-dimensional rarefied gas flows subject to boundary induced discontinuities

Cited by 25 publications

References 27 publications

Sound propagation through a rarefied gas in rectangular channels

Sound propagation through a rarefied gas in rectangular channels

Solving the Boltzmann equation on GPUs

Simulation of transport phenomena in conditions far from thermodynamic equilibrium via kinetic theory with applications in vacuum technology and MEMS

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