scholarly journals Stationary solutions of incompressible viscous flow in a wall-driven semi-circular cavity

2021 ◽  
Vol 61 (4) ◽  
pp. 516-525
Author(s):  
Ercan Erturk
Keyword(s):  
Viscous Flow ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Stationary Solutions ◽  
Navier Stokes ◽  
Circular Cavity ◽  
Primary Vortex ◽  
Navier Stokes Equations ◽  
Incompressible Viscous Flow ◽  
Vortex Centre

Stationary numerical solutions of incompressible viscous flow inside a wall-driven semicircular cavity are presented. After a conformal mapping of the geometry, using a body-fitted mesh, the Navier-Stokes equations are solved numerically. The stationary solutions of the flow in a wall-driven semi-circular cavity are computed up to Re = 24000. The present results are in good agreement with the published results found in the literature. Our results show that as the Reynolds number increases, the sizes of the secondary and tertiary vortices increase, whereas the size of the primary vortex decreases. At large Reynolds numbers, the vorticity at the primary vortex centre increases almost linearly stating that Batchelor’s mean-square law is not valid for wall-driven semi-circular cavity flow. Detailed results are presented and also tabulated for future references and benchmark purposes.

Numerical investigation of the steady viscous flow past a stationary deformable bubble

1985 ◽  
Vol 158 ◽  
pp. 341-364 ◽  
Author(s):  
C. I. Christov ◽  
P. K. Volkov
Keyword(s):  
Viscous Flow ◽  
Stokes Equations ◽  
Moving Boundaries ◽  
Navier Stokes ◽  
Toroidal Vortex ◽  
Navier Stokes Equations ◽  
Flow Past ◽  
Incompressible Viscous Flow ◽  
Experimental Works ◽  
The Common

A method for solving the Navier–Stokes equations in domains with moving boundaries is proposed. By means of a coordinate transformation, the region under consideration is converted to a region with known boundaries which are coordinate surfaces. An appropriate difference scheme with an algorithm for its implementation is constructed. The method is applied to the case of steady incompressible viscous flow past a resting deformable bubble. Results are obtained for wide ranges for Reynolds and Weber numbers and compared with other theoretical or experimental works in the common regions for the governing parameters. A separation of the flow and the occurrence of a toroidal vortex in the rear of the bubble is observed and verified through a number of computations. Typical flow patterns as well as a variety of practically important relations between the parameters of the flow are shown graphically.

scholarly journals Two-dimensional incompressible viscous flow around a thin obstacle tending to a curve

2009 ◽  
Vol 139 (6) ◽  
pp. 1237-1254 ◽  
Author(s):  
Christophe Lacave
Keyword(s):  
Viscous Fluid ◽  
Viscous Flow ◽  
Recent Work ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Incompressible Viscous Flow ◽  
Limit Solution ◽  
Thin Obstacle

Building on a recent work, we consider a two-dimensional viscous fluid in the exterior of a thin obstacle shrinking to a curve, proving convergence to a solution of the Navier–Stokes equations in the exterior of a curve. The uniqueness of the limit solution is also shown.>

scholarly journals Direct Simulation of Low-Re Flow around a Square Cylinder by Numerical Manifold Method for Navier-Stokes Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Zhengrong Zhang ◽  
Xiangwei Zhang
Keyword(s):  
Viscous Flow ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Numerical Manifold Method ◽  
Square Cylinder ◽  
Navier Stokes Equations ◽  
Weighted Residuals ◽  
Numerical Tests ◽  
Incompressible Viscous Flow ◽  
Numerical Manifold

Numerical manifold method was applied to directly solve Navier-Stokes (N-S) equations for incompressible viscous flow in this paper, and numerical manifold schemes for N-S equations coupled velocity and pressure were derived based on Galerkin weighted residuals method as well. Mixed cover with linear polynomial function for velocity and constant function for pressure was employed in finite element cover system. As an application, mixed cover 4-node rectangular manifold element has been used to simulate the incompressible viscous flow around a square cylinder in a channel. Numerical tests illustrate that NMM is an effective and high-order accurate numerical method for incompressible viscous flow N-S equations.

scholarly journals Simulation of Free Airfoil Vibrations in Incompressible Viscous Flow — Comparison of FEM and FVM

10.14311/1690 ◽  
2012 ◽  
Vol 52 (6) ◽  
Author(s):  
Petr Sváček ◽  
Jaromír Horáček ◽  
Radek Honzátko ◽  
Karel Kozel
Keyword(s):  
Viscous Flow ◽  
Degrees Of Freedom ◽  
Stokes Equations ◽  
Vertical Direction ◽  
Navier Stokes ◽  
Computational Domain ◽  
Arbitrary Lagrangian Eulerian ◽  
Navier Stokes Equations ◽  
Incompressible Viscous Flow ◽  
Naca 0012

This paper deals with a numerical solution of the interaction of two-dimensional (2-D) incompressible viscous flow and a vibrating profile NACA 0012 with large amplitudes. The laminar flow is described by the Navier-Stokes equations in the arbitrary Lagrangian-Eulerian form. The profile with two degrees of freedom (2-DOF) can rotate around its elastic axis and oscillate in the vertical direction. Its motion is described by a nonlinear system of two ordinary differential equations. Deformations of the computational domain due to the profile motion are treated by the arbitrary Lagrangian-Eulerianmethod. The finite volume method and the finite element method are applied, and the numerical results are compared.

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