Implementation of slip boundary conditions in the finite volume method: new techniques

When modeling rarefied gas flows, continuous approximation is limited by the Knudsen regime. The presented cold gas thruster for space applications is investigated for pressure values lying between 10−2 and 103 Pa. It is comprised of a subsonic funnel region, a transsonic region consisting of a ring-shaped nozzle throat and a supersonic diffuser region. Diffusive and specular / mirror reflection is used to describe the behavior of particle/wall collision in the discrete model. Simulation results are compared both with experimental data and with numerical results computed using a finite-volume method. The transsonic flow through the nozzle throat shows very good agreement with experimental data. Simulation and experimental results emphasize the influence of various geometric factors like size and shape of the nozzle throat. Furthermore, differences in the acceleration behavior of Argon and Xenon are examined. Results of simulations utilizing the DSMC method [Bird, 1994, Stefanov et al., 2011] with diffusively reflecting boundary conditions present the best agreement with experimental data. Any deviation seen using the finite-volume method with no-slip boundary conditions can be explained by the equilibrium gas-state near the walls [Brenner, 2005, Greenshields et al., 2007]. The non-equilibrium approach produces lower velocity gradients near the wall, especially in wall regions with high levels of surface curvature.

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Computation of Rarefied Gaseous Flows in Micro to Nano Scale Channels With Slip to Transient Regimes Using General Second-Order Quadratic Elements

ASME 2008 6th International Conference on Nanochannels, Microchannels, and Minichannels ◽

10.1115/icnmm2008-62155 ◽

2008 ◽

Author(s):

M. Darbandi ◽

Y. Daghighi

Keyword(s):

Boundary Conditions ◽

Finite Volume ◽

Higher Order ◽

Second Order ◽

Navier Stokes ◽

Computational Domain ◽

Slip Boundary Conditions ◽

Slip Boundary ◽

Nano Scale ◽

Transient Regimes

A new finite-volume-based finite-element method using the quadratic elements is developed in the present study, to analyze the flow in micro and nano sizes with higher-order slip boundary conditions. The method is applied to gaseous flow in micro and nanoscale-channels. The developed method is carried out over a wide range of Knudsen numbers, which cover not only the continuum slip flow regime with 0≤Kn≤0.1 but also it entire the range of transient regime with 0.1<Kn≤10. To make the present computational model capable of simulating micro and nano sizes with the help of the Navier-Stokes equations, the modified high-order slip boundary conditions are applied which need utilizing the advantages of general quadratic second order elements in the computational domain. In other words, this paper introduces a new developed method, which is applied on higher-order elements, and employing reliable boundary conditions that all of these issues are used for the first time in the Micro/Nano study as well. The results reveal excellent agreement with those represented by analytical, DSMC, and Boltzmann calculations. The proposed method (using finite-volume-element strategy which benefits from the advantages of general quadratic second-order elements) is proved to be an efficient, practical, and accurate tool, which robustly extends the capability of our primitive large scale Navier-Stokes solver to micro and nano-scale flow predictions in slip and transient regimes. It can be regarded as a super alternative to classical molecular dynamics-based methods.

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A compact finite volume method and its extrapolation for elliptic equations with third boundary conditions

Applied Mathematics and Computation ◽

10.1016/j.amc.2015.04.087 ◽

2015 ◽

Vol 264 ◽

pp. 258-271 ◽

Cited By ~ 1

Author(s):

Tongke Wang ◽

Zhiyue Zhang

Keyword(s):

Boundary Conditions ◽

Finite Volume Method ◽

Finite Volume ◽

Elliptic Equations ◽

Volume Method

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The high hall ventilation with the simplified simulation of the fan

EPJ Web of Conferences ◽

10.1051/epjconf/201818002051 ◽

2018 ◽

Vol 180 ◽

pp. 02051

Author(s):

Martin Kyncl ◽

Jaroslav Pelant

Keyword(s):

Numerical Simulation ◽

Gravitational Field ◽

Boundary Conditions ◽

Finite Volume Method ◽

Riemann Problem ◽

Finite Volume ◽

Unstructured Meshes ◽

System Of Equations ◽

Computational Results ◽

Volume Method

Here we work with the system of equations describing the non-stationary compressible turbulent multi-component flow in the gravitational field. We focus on the numerical simulation of the fan situated inside the high hall. The RANS equations are discretized with the use of the finite volume method. The original modification of the Riemann problem and its solution is used at the boundaries. The combination of specific boundary conditions is used for the simulation of the fan. The presented computational results are computed with own-developed code (C, FORTRAN, multiprocessor, unstructured meshes in general).

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