Analysis and accurate numerical solutions of the integral equation derived from the linearized BGKW equation for the steady Couette flow
Shidong Jiang,Li-Shi Luo +1 more
TLDR
The integral equation for the flow velocity u ( x ; k ) in the steady Couette flow derived from the linearized Bhatnagar-Gross-Krook-Welander kinetic equation is studied in detail both theoretically and numerically in a wide range of the Knudsen number k between 0.003 and 100.0.About:
This article is published in Journal of Computational Physics.The article was published on 2016-07-01 and is currently open access. It has received 31 citations till now. The article focuses on the topics: Summation equation & Integral equation.read more
Citations
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Accurate and efficient computation of the Boltzmann equation for Couette flow: Influence of intermolecular potentials on Knudsen layer function and viscous slip coefficient
TL;DR: A novel synthetic iteration scheme (SIS) is developed for the LBE to find solutions of Couette flow accurately and efficiently and it is found that the whole Knudsen layer function can be well fitted by the power series.
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Fast Convergence and Asymptotic Preserving of the General Synthetic Iterative Scheme
Wei Su,Lianhua Zhu,Lei Wu +2 more
TL;DR: The rigorous proof of both property indicates that the error decay rate between two consecutive iterations decreases to zero with $K$, while the second implies that the GSIS is asymptotically preserving the Navier-Stokes limit.
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Effective mean free path and viscosity of confined gases
TL;DR: In this paper, the molecular mean free path (MFP) of gases in confined geometries is numerically evaluated by means of the direct simulation Monte Carlo method and molecular dynamics simulations.
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Half-range lattice Boltzmann models for the simulation of Couette flow using the Shakhov collision term
TL;DR: In this article, mixed lattice Boltzmann models are used to simulate rarefied Couette flows between parallel plates. But the authors find that recovering the nonlinear part of the velocity profile (i.e., its deviation from a linear function) at the Knudsen number (kn) ≥ 0.1 requires high quadrature orders, and they attribute these deviations to the limited applicability of the Shakhov collision model for highly out of equilibrium flows.
References
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Book
Table of Integrals, Series, and Products
TL;DR: Combinations involving trigonometric and hyperbolic functions and power 5 Indefinite Integrals of Special Functions 6 Definite Integral Integral Functions 7.Associated Legendre Functions 8 Special Functions 9 Hypergeometric Functions 10 Vector Field Theory 11 Algebraic Inequalities 12 Integral Inequality 13 Matrices and related results 14 Determinants 15 Norms 16 Ordinary differential equations 17 Fourier, Laplace, and Mellin Transforms 18 The z-transform
A table of integrals
TL;DR: Basic Forms x n dx = 1 n + 1 x n+1 (1) 1 x dx = ln |x| (2) udv = uv − vdu (3) 1 ax + bdx = 1 a ln|ax + b| (4) Integrals of Rational Functions
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Handbook of Mathematical Functions with Formulas
TL;DR: The Handbook of Mathematical Functions with Formulas (HOFF-formulas) as mentioned in this paper is the most widely used handbook for mathematical functions with formulas, which includes the following:
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A Model for Collision Processes in Gases. I. Small Amplitude Processes in Charged and Neutral One-Component Systems
TL;DR: In this paper, a kinetic theory approach to collision processes in ionized and neutral gases is presented, which is adequate for the unified treatment of the dynamic properties of gases over a continuous range of pressures from the Knudsen limit to the high pressure limit where the aerodynamic equations are valid.