Computations of the Flow and Heat Transfer in Microdevices Using DSMC With Implicit Boundary Conditions

2001 ◽  
Vol 124 (2) ◽  
pp. 338-345 ◽  
Author(s):  
Yichuan Fang ◽  
William W. Liou
Keyword(s):  
Heat Transfer ◽  
Fluid Dynamics ◽  
Boundary Conditions ◽  
Microelectromechanical Systems ◽  
Stokes Equations ◽  
Direct Simulation Monte Carlo ◽  
Velocity Slip ◽  
Navier Stokes ◽  
Slip Boundary ◽  
Calculated Velocity

The heat transfer and the fluid dynamics characteristics of subsonic gas flows through microchannels are examined using the direct simulation Monte Carlo (DSMC) method. A simple implicit treatment for the low-speed inflow and outflow boundaries for the DSMC of the flows in microelectromechanical systems (MEMS) is used. Micro-Couette flows and micro-Poiseuille flows are simulated with the value of the Knudsen numbers ranging between 0.06 and 0.72. Where appropriate, the calculated velocity slip and temperature distribution are compared with analytical solutions derived from the Navier-Stokes equations with slip-boundary conditions. A patterned microstructure with nonuniform surface temperature is also simulated. The computational results show that the Knudsen number and the geometric complexity have significant effects on the heat transfer as well as the fluid dynamics properties of the microfluid flows studied.

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 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.

scholarly journals Slip Boundary Conditions for the Compressible Navier–Stokes Equations

2017 ◽  
Vol 169 (4) ◽  
pp. 744-781 ◽  
Author(s):  
Kazuo Aoki ◽  
Céline Baranger ◽  
Masanari Hattori ◽  
Shingo Kosuge ◽  
Giorgio Martalò ◽  
...  
Keyword(s):  
Boundary Conditions ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Slip Boundary Conditions ◽  
Navier Stokes Equations ◽  
Slip Boundary
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