scholarly journals Uniform estimates for Stokes equations in a domain with a small hole and applications in homogenization problems

2021 ◽  
Vol 60 (6) ◽  
Author(s):  
Yong Lu
Keyword(s):  
Stokes Equations ◽  
Small Hole ◽  
Uniform Estimates ◽  
Homogenization Problems

UNIFORM ESTIMATES FOR TRANSPORT-DIFFUSION EQUATIONS

2007 ◽  
Vol 04 (01) ◽  
pp. 1-17 ◽  
Author(s):  
R. DANCHIN
Keyword(s):  
Reynolds Number ◽  
Vector Field ◽  
Fluid Mechanics ◽  
Incompressible Fluid ◽  
High Reynolds Number ◽  
Stokes Equations ◽  
Diffusion Equations ◽  
Uniform Estimates ◽  
Transport Diffusion ◽  
High Reynolds

We prove new estimates in Besov spaces [Formula: see text] or [Formula: see text] for transport-diffusion equations. Comparing with previous works, there is no restriction on the index p (hence our estimates apply in Hölder spaces) and the transport vector-field need not be divergence-free. Besides, similar estimates can be proved for the non-stationary Stokes equations with convection. We expect our results to be useful for studying compressible or incompressible fluid mechanics with high Reynolds number.

Unsteady flow of a viscous fluid from a source in a wall

1970 ◽  
Vol 41 (3) ◽  
pp. 641-652 ◽  
Author(s):  
E. O. Tuck
Keyword(s):  
Viscous Fluid ◽  
Unsteady Flow ◽  
Line Source ◽  
Stokes Equations ◽  
Rigid Wall ◽  
Small Hole ◽  
Navier Stokes ◽  
Navier Stokes Equations

A problem with possible physiological applications concerns the escape of a viscous fluid through a small hole in a wall. The solution presented here is for a line source of sinusoidally pulsating strength located at the originx=y= 0, where the planey= 0 is a rigid wall and the fluid is at rest aty= + ∞. The linearized Navier—Stokes equations are solved, and results in the form of streamline plots are shown and discussed.

scholarly journals Low Mach number limit for the compressible Navier–Stokes equations with density-dependent viscosity and vorticity-slip boundary condition

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Dandan Ren ◽  
Yunting Ding ◽  
Xinfeng Liang
Keyword(s):  
Boundary Condition ◽  
Mach Number ◽  
Stokes Equations ◽  
Slip Boundary Condition ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Density Dependent ◽  
Uniform Estimates ◽  
Slip Boundary ◽  
Dependent Viscosity

Abstract In this paper, we consider the three-dimensional compressible Navier–Stokes equations with density-dependent viscosity and vorticity-slip boundary condition in a bounded smooth domain. The main idea is to derive the uniform estimates for both time and the Mach number. The difficulty is dealing with density-dependent viscosity terms carefully. With the uniform estimates, we can verify the low Mach limit of the global strong solutions of compressible Navier–Stokes equations and the global existence and uniqueness of the strong solution of incompressible Navier–Stokes equations around a steady state.

CLASSICAL SOLVABILITY AND UNIFORM ESTIMATES FOR THE STEADY STOKES SYSTEM IN DOMAINS WITH NONCOMPACT BOUNDARIES

1996 ◽  
Vol 06 (02) ◽  
pp. 149-167 ◽  
Author(s):  
K. PILECKAS
Keyword(s):  
Incompressible Fluid ◽  
Coordinate System ◽  
Lipschitz Condition ◽  
Stokes System ◽  
Stokes Equations ◽  
Viscous Incompressible Fluid ◽  
Uniform Estimates ◽  
Classical Solvability ◽  
Weighted Hölder Spaces ◽  
Pointwise Decay

The stationary Stokes equations of a viscous incompressible fluid are considered in domains Ω with m > 1 outlets to infinity, which have in some coordinate system the following form [Formula: see text] where gi are functions satisfying the global Lipschitz condition and g'i (xn) → 0 as xn → ∞. In this paper we prove the solvability of the Stokes system with prescribed fluxes in weighted Hölder spaces and we show the pointwise decay of the solutions.

Advanced TEM sample preparation techniques for submicron Si devices

1995 ◽  
Vol 53 ◽  
pp. 516-517 ◽  
Author(s):  
P. B. Basham ◽  
H. L. Tsai
Keyword(s):  
Sample Preparation ◽  
Process Development ◽  
Light Transmission ◽  
Specific Area ◽  
Turnaround Time ◽  
Small Hole ◽  
Area Of Interest ◽  
Transmission Electron ◽  
Polished Side ◽  
Preparation Techniques

The use of transmission electron microscopy (TEM) to support process development of advanced microelectronic devices is often challenged by a large amount of samples submitted from wafer fabrication areas and specific-spot analysis. Improving the TEM sample preparation techniques for a fast turnaround time is critical in order to provide a timely support for customers and improve the utilization of TEM. For the specific-area sample preparation, a technique which can be easily prepared with the least amount of effort is preferred. For these reasons, we have developed several techniques which have greatly facilitated the TEM sample preparation.For specific-area analysis, the use of a copper grid with a small hole is found to be very useful. With this small-hole grid technique, TEM sample preparation can be proceeded by well-established conventional methods. The sample is first polished to the area of interest, which is then carefully positioned inside the hole. This polished side is placed against the grid by epoxy Fig. 1 is an optical image of a TEM cross-section after dimpling to light transmission.

Effects of stator splitter blades on aerodynamic performance of a single-stage transonic axial compressor

2020 ◽  
Vol 14 (4) ◽  
pp. 7369-7378
Author(s):  
Ky-Quang Pham ◽  
Xuan-Truong Le ◽  
Cong-Truong Dinh
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Axial Compressor ◽  
Aerodynamic Performance ◽  
Numerical Results ◽  
Single Stage ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Operating Stability ◽  
Length Coverage

Splitter blades located between stator blades in a single-stage axial compressor were proposed and investigated in this work to find their effects on aerodynamic performance and operating stability. Aerodynamic performance of the compressor was evaluated using three-dimensional Reynolds-averaged Navier-Stokes equations using the k-e turbulence model with a scalable wall function. The numerical results for the typical performance parameters without stator splitter blades were validated in comparison with experimental data. The numerical results of a parametric study using four geometric parameters (chord length, coverage angle, height and position) of the stator splitter blades showed that the operational stability of the single-stage axial compressor enhances remarkably using the stator splitter blades. The splitters were effective in suppressing flow separation in the stator domain of the compressor at near-stall condition which affects considerably the aerodynamic performance of the compressor.

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