Prediction of inverted velocity profile for gas flow in nanochannel

2014 ◽  
Vol 28 (29) ◽  
pp. 1450227
Author(s):  
T. T. Zhang ◽  
Y. R. Ren
Keyword(s):  
Gas Flow ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Analysis Method ◽  
Slip Boundary Conditions ◽  
Interesting Phenomenon ◽  
Navier Stokes Equations ◽  
Velocity Inversion ◽  
Slip Boundary ◽  
Homotopy Analysis

Velocity inversion is an interesting phenomenon of nanoscale which means that the velocity near the wall is greater than that of center. To solve this problem, fluid flow in nanochannel attracts more attention in recent years. The physical model of gas flow in two-dimensional nanochannel was established here. To describe the process with conventional control equations, Navier–Stokes equations combined with high-order accurate slip boundary conditions was used as mathematical model. With the introduction of new dimensionless variables, the problem was reduced to an ordinary differential equation. Then it was analytically solved and investigated using homotopy analysis method (HAM). The results were verified by comparing with other available experiment data. Result shows that the proposed method could predict velocity phenomenon.

Parallel iterative finite-element algorithms for the Navier–Stokes equations with nonlinear slip boundary conditions

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Kangrui Zhou ◽  
Yueqiang Shang
Keyword(s):  
Finite Element ◽  
Boundary Conditions ◽  
Parallel Algorithms ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Slip Boundary Conditions ◽  
Navier Stokes Equations ◽  
Slip Boundary ◽  
Parallel Iterative ◽  
Nonlinear Slip Boundary Conditions

AbstractBased on full domain partition, three parallel iterative finite-element algorithms are proposed and analyzed for the Navier–Stokes equations with nonlinear slip boundary conditions. Since the nonlinear slip boundary conditions include the subdifferential property, the variational formulation of these equations is variational inequalities of the second kind. In these parallel algorithms, each subproblem is defined on a global composite mesh that is fine with size h on its subdomain and coarse with size H (H ≫ h) far away from the subdomain, and then we can solve it in parallel with other subproblems by using an existing sequential solver without extensive recoding. All of the subproblems are nonlinear and are independently solved by three kinds of iterative methods. Compared with the corresponding serial iterative finite-element algorithms, the parallel algorithms proposed in this paper can yield an approximate solution with a comparable accuracy and a substantial decrease in computational time. Contributions of this paper are as follows: (1) new parallel algorithms based on full domain partition are proposed for the Navier–Stokes equations with nonlinear slip boundary conditions; (2) nonlinear iterative methods are studied in the parallel algorithms; (3) new theoretical results about the stability, convergence and error estimates of the developed algorithms are obtained; (4) some numerical results are given to illustrate the promise of the developed algorithms.

scholarly journals Generalized Navier–Stokes equations with nonlinear anisotropic viscosity

2019 ◽  
Vol 17 (06) ◽  
pp. 977-1003
Author(s):  
H. B. de Oliveira
Keyword(s):  
Stokes Equations ◽  
Fluid Flows ◽  
Ekman Layer ◽  
Navier Stokes ◽  
Slip Boundary Conditions ◽  
Very Weak Solutions ◽  
Navier Stokes Equations ◽  
Slip Boundary ◽  
Nonlinear Viscosity ◽  
Anisotropic Viscosity

The purpose of this work is to study the generalized Navier–Stokes equations with nonlinear viscosity that, in addition, can be fully anisotropic. Existence of very weak solutions is proved for the associated initial and boundary-value problem, supplemented with no-slip boundary conditions. We show that our existence result is optimal in some directions provided there is some compensation in the remaining directions. A particular simplification of the problem studied here, reduces to the Navier–Stokes equations with (linear) anisotropic viscosity used to model either the turbulence or the Ekman layer in atmospheric and oceanic fluid flows.

scholarly journals Regularity Criteria for Navier-Stokes Equations with Slip Boundary Conditions on Non-flat Boundaries via Two Velocity Components

2019 ◽  
Vol 9 (1) ◽  
pp. 633-643
Author(s):  
Hugo Beirão da Veiga ◽  
Jiaqi Yang
Keyword(s):  
Boundary Conditions ◽  
Stokes Equations ◽  
Slip Boundary Condition ◽  
Regularity Criteria ◽  
Navier Stokes ◽  
Slip Boundary Conditions ◽  
Navier Stokes Equations ◽  
Slip Boundary ◽  
Whole Space ◽  
Space Case

Abstract H.-O. Bae and H.J. Choe, in a 1997 paper, established a regularity criteria for the incompressible Navier-Stokes equations in the whole space ℝ3 based on two velocity components. Recently, one of the present authors extended this result to the half-space case $\begin{array}{} \displaystyle \mathbb{R}^3_+ \end{array}$. Further, this author in collaboration with J. Bemelmans and J. Brand extended the result to cylindrical domains under physical slip boundary conditions. In this note we obtain a similar result in the case of smooth arbitrary boundaries, but under a distinct, apparently very similar, slip boundary condition. They coincide just on flat portions of the boundary. Otherwise, a reciprocal reduction between the two results looks not obvious, as shown in the last section below.

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