On the inviscid limit for the solutions of two-dimensional incompressible Navier–Stokes equations with slip-type boundary conditions

Nonlinearity ◽  
2006 ◽  
Vol 19 (6) ◽  
pp. 1349-1363 ◽  
Author(s):  
Walter M Rusin
Keyword(s):  
Boundary Conditions ◽  
Stokes Equations ◽  
Inviscid Limit ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Type Boundary

scholarly journals A Note on the Vanishing Viscosity Limit in the Yudovich Class

2020 ◽  
pp. 1-11
Author(s):  
Christian Seis
Keyword(s):  
Stokes Equations ◽  
Velocity Fields ◽  
Inviscid Limit ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Vanishing Viscosity ◽  
Navier Stokes Equations ◽  
Vanishing Viscosity Limit ◽  
Viscosity Limit ◽  
The Difference

Abstract We consider the inviscid limit for the two-dimensional Navier–Stokes equations in the class of integrable and bounded vorticity fields. It is expected that the difference between the Navier–Stokes and Euler velocity fields vanishes in $L^2$ with an order proportional to the square root of the viscosity constant $\nu $ . Here, we provide an order $ (\nu /|\log \nu | )^{\frac 12\exp (-Ct)}$ bound, which slightly improves upon earlier results by Chemin.

scholarly journals Computer Simulation of Water Flow Animation Based on Two-Dimensional Navier-Stokes Equations

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Rushi Cao ◽  
Ruyun Cao
Keyword(s):  
Computer Graphics ◽  
Boundary Conditions ◽  
Water Flow ◽  
Stokes Equations ◽  
Simulation Method ◽  
Fluid Simulation ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equation ◽  
Navier Stokes Equations

Simulation of water flow animation is a significant and challenging subject in computer graphics. With the continuous development of computational fluid dynamics and computer graphics, many more effective simulation methods have been developed, and fluid animation simulation has developed rapidly. In order to obtain realistic flow animation, one of the key aspects is to simulate flow motion. Based on the two-dimensional Navier-Stokes equations, a mathematical model is established to solve the boundary conditions required by the physical flow field of water. The coordinate transformation formula is introduced to transform the irregular physical area into a regular square calculation area, and then, the specific expressions of the liberalized Navier-Stokes equation, continuity equation, pressure Poisson equation, and dimensionless boundary conditions are given. Using animation software to sequence graphics and images of all kinds of control and direct operation of the relevant instructions, through the computer technology to simulate the flow of animation, based on the stability of fluid simulation method and simulation efficiency, so as to make realistic flow animation. The results show that FluidsNet has considerable performance in accelerating large scene animation simulation on the basis of ensuring the rationality of prediction, and the motion of water wave is realistic. The application of computer successfully simulates water flow.

Non-linear effects in steady supersonic dissipative gasdynamics Part 1. Two-dimensional flow

1971 ◽  
Vol 50 (1) ◽  
pp. 161-176 ◽  
Author(s):  
T. H. Chong ◽  
L. Sirovich
Keyword(s):  
Stokes Equations ◽  
Inviscid Limit ◽  
Navier Stokes ◽  
Thin Body ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Non Linear ◽  
Two Dimensional Flow ◽  
Linear Effects ◽  
And Diffusion

Steady supersonic two-dimensional flows governed by the Navier–Stokes equations are considered. For flows past a thin body, the Oseen theory is shown to fail at large distances. An investigation of the equations bridging the linear and non-linear zones is made. From this, it follows that the resulting equations are a system of Burgers and diffusion equations. The Whitham theory is shown to result under the inviscid limit of our analysis. Various other limits are also obtained.An explicit expression for flows past a thin airfoil is given, and the flow past a double wedge is exhibited in terms of known functions.

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