scholarly journals Solution of Time Periodic Electroosmosis Flow with Slip Boundary

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Qian Sun ◽  
Yonghong Wu ◽  
Lishan Liu ◽  
B. Wiwatanapataphee
Keyword(s):  
Boundary Conditions ◽  
Exact Solutions ◽  
Solid Surface ◽  
Electroosmotic Flow ◽  
Mixing Enhancement ◽  
Slip Boundary Conditions ◽  
Slip Boundary ◽  
Flow Problems ◽  
Micrometer Scale ◽  
Time Periodic

Recent research confirms that slip of a fluid on the solid surface occurs at micrometer scale. Slip on solid surface may cause the change of interior material deformation which consequently leads to the change of velocity profile and stress field. This paper concerns the time periodic electroosmotic flow in a channel with slip boundary driven by an alternating electric field, which arises from the study of particle manipulation and separation such as flow pumping and mixing enhancement. Although exact solutions to various flow problems of electroosmotic flows under the no-slip condition have been obtained, exact solutions for problems under slip boundary conditions have seldom been addressed. In this paper, an exact solution is derived for the time periodic electroosmotic flow in two-dimensional straight channels under slip boundary conditions.

Linearized no-slip boundary conditions at a rough surface

2013 ◽  
Vol 737 ◽  
pp. 349-367 ◽  
Author(s):  
Paolo Luchini
Keyword(s):  
Aspect Ratio ◽  
Boundary Conditions ◽  
Solid Wall ◽  
Stokes Problem ◽  
Far Field ◽  
Slip Boundary Conditions ◽  
Transition Prediction ◽  
Slip Boundary ◽  
Flow Problems ◽  
Field Behaviour

AbstractLinearized boundary conditions are a commonplace numerical tool in any flow problems where the solid wall is nominally flat but the effects of small waviness or roughness are being investigated. Typical examples are stability problems in the presence of undulated walls or interfaces, and receptivity problems in aerodynamic transition prediction or turbulent flow control. However, to pose such problems properly, solutions in two mathematical distinguished limits have to be considered: a shallow-roughness limit, where not only roughness height but also its aspect ratio becomes smaller and smaller, and a small-roughness limit, where the size of the roughness tends to zero but its aspect ratio need not. Here a connection between the two solutions is established through an analysis of their far-field behaviour. As a result, the effect of the surface in the small-roughness limit, obtained from a numerical solution of the Stokes problem, can be recast as an equivalent shallow-roughness linearized boundary condition corrected by a suitable protrusion coefficient (related to the protrusion height used years ago in the study of riblets) and a proximity coefficient, accounting for the interference between multiple protrusions in a periodic array. Numerically computed plots and interpolation formulas of such correction coefficients are provided.

Numerical Solution of Reynolds Equation With Slip Boundary Conditions for Cases of Large Bearing Number (Λ > 300)

1979 ◽  
Vol 101 (1) ◽  
pp. 64-66 ◽  
Author(s):  
A. Sereny ◽  
V. Castelli
Keyword(s):  
Boundary Layer ◽  
Boundary Conditions ◽  
Exact Solutions ◽  
Numerical Solution ◽  
Reynolds Equation ◽  
Slip Boundary Conditions ◽  
Grid Spacing ◽  
Slip Boundary ◽  
Finite Differencing ◽  
Bearing Number

The behavior of two numerical discretizations for the solution of Reynolds equation with slip boundary conditions for cases of large bearing number is described. The narrow boundary layer caused by the large bearing number is well handled by a variable grid spacing. The performance of these methods is compared against exact solutions for the ∞-wide case. It is clearly demonstrated that discretization which satisfies integral conservation is preferable to the differential procedure of finite differencing.

scholarly journals Asymptotic analysis of an optimal control problem for a viscous incompressible fluid with Navier slip boundary conditions

2021 ◽  
pp. 1-21
Author(s):  
Claudia Gariboldi ◽  
Takéo Takahashi
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Boundary Conditions ◽  
Control Problem ◽  
Stokes System ◽  
Navier Stokes ◽  
Slip Boundary Conditions ◽  
Navier Slip ◽  
Slip Boundary ◽  
Navier Slip Boundary Conditions

We consider an optimal control problem for the Navier–Stokes system with Navier slip boundary conditions. We denote by α the friction coefficient and we analyze the asymptotic behavior of such a problem as α → ∞. More precisely, we prove that if we take an optimal control for each α, then there exists a sequence of optimal controls converging to an optimal control of the same optimal control problem for the Navier–Stokes system with the Dirichlet boundary condition. We also show the convergence of the corresponding direct and adjoint states.

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.

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