scholarly journals Numerical Simulation of Slip effect on Lid-Driven Cavity Flow Problem for High Reynolds Number: Vorticity – Stream Function Approach

2021 ◽  
Vol 8 (3) ◽  
pp. 418-424
Author(s):  
Syed Fazuruddin ◽  
Seelam Sreekanth ◽  
G. Sankara Sekhar Raju
Keyword(s):  
Reynolds Number ◽  
Stream Function ◽  
Stokes Equations ◽  
Cavity Flow ◽  
Partial Slip ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Driven Cavity ◽  
Slip Conditions ◽  
Driven Cavity Flow

Incompressible 2-D Navier-stokes equations for various values of Reynolds number with and without partial slip conditions are studied numerically. The Lid-Driven cavity (LDC) with uniform driven lid problem is employed with vorticity - Stream function (VSF) approach. The uniform mesh grid is used in finite difference approximation for solving the governing Navier-stokes equations and developed MATLAB code. The numerical method is validated with benchmark results. The present work is focused on the analysis of lid driven cavity flow of incompressible fluid with partial slip conditions (imposed on side walls of the cavity). The fluid flow patterns are studied with wide range of Reynolds number and slip parameters.

scholarly journals Numerical Implementations for 2D Lid-Driven Cavity Flow in Stream Function Formulation

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
K. Poochinapan
Keyword(s):  
Reynolds Number ◽  
Stream Function ◽  
Stokes Equations ◽  
Operator Splitting ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Driven Cavity ◽  
Function Formulation ◽  
High Reynolds ◽  
Stream Function Formulation

The aim of this paper is to study the properties of approximations to nonlinear terms of the 2D incompressible Navier-Stokes equations in the stream function formulation (time-dependent biharmonic equation). The nonlinear convective terms are numerically solved by using the method with internal iterations, compared to the ones which are solved by using explicit and implicit schemes (operator splitting scheme Christov and Marinova; (2001)). Using schemes and algorithms, the steady 2D incompressible flow in a lid-driven cavity is solved up to Reynolds number Re =5000 with second-order spatial accuracy. The schemes are thoroughly validated on grids with different resolutions. The result of numerical experiments shows that the finite difference scheme with internal iterations on nonlinearity is more efficient for the high Reynolds number.

Laminar Incompressible Recirculating Flow in a Driven Cavity of Polar Cross Section

1977 ◽  
Vol 99 (4) ◽  
pp. 774-777 ◽  
Author(s):  
U. Ghia ◽  
R. K. Goyal
Keyword(s):  
Stream Function ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Cavity Flow ◽  
Rectangular Cavity ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Driven Cavity ◽  
Recirculating Flow ◽  
Alternating Direction

The driven flow in a polar cavity has been analyzed using the complete Navier-Stokes equations formulated in terms of a stream function and vorticity. An alternating-direction implicit method, with careful treatment of the convective terms in the equations, is used to obtain the numerical solutions. Results are obtained for the stream function, vorticity, velocities and pressure for various values of the two characteristic parameters of the problem, namely, the flow Reynolds number Re and the aspect ratio of the cavity. The formulation is general and produces results for the driven rectangular cavity-flow problem as a special case. Good agreement is obtained between the present solutions for this case and available corresponding results. The overall features of the driven polar-cavity flow are found to be generally similar to those for the rectangular cavity.

Flow Pattern on the Surface of Airfoil With Lower Reynolds Number

2009 ◽  
Author(s):  
Xu Sun ◽  
Jia-Zhong Zhang
Keyword(s):  
Reynolds Number ◽  
Flow Pattern ◽  
Stokes Equations ◽  
Separation Bubble ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Driven Cavity ◽  
Naca0012 Airfoil ◽  
Lower Reynolds Number ◽  
Characteristic Based Split

In this paper, aerodynamic performance of the NACA0012 airfoil in the incompressible flow with a lower Reynolds number (Re) is investigated numerically from the viewpoints of flow pattern and nonlinear dynamics. First, the characteristic-based split (CBS) finite element method is introduced for the approximation of the incompressible Navier-Stokes equations, and then the lid-driven cavity flow and flow around a circular cylinder are calculated for varification. Then, at Re = 1000, flow fields around the NACA0012 airfoil at a series of angles of attack are simulated. With the increase of the attack angle, great change of the flow pattern appears, and the flow structures such as trailing edge vortex, separation bubble and shedding vortex are observed. Moreover, it is found that the separation bubble plays an important role in the deterioration of the flow stability at higher attack angles, and the vortex shedding can be taken as the result of a Hopf bifurcation while the bifurcation parameter is the angle of attack.

A PLATFORM FOR DEVELOPING NEW LATTICE BOLTZMANN MODELS

2005 ◽  
Vol 16 (01) ◽  
pp. 61-84 ◽  
Author(s):  
H. W. ZHENG ◽  
C. SHU ◽  
Y. T. CHEW ◽  
J. QIU
Keyword(s):  
Lattice Boltzmann ◽  
Stokes Equations ◽  
Cavity Flow ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Driven Cavity ◽  
Velocity Models ◽  
Equilibrium Function ◽  
New Models ◽  
Lattice Boltzmann Models

This paper presents a platform to develop new lattice Boltzmann models. It gives a general framework for different applications. It also presents basic velocity models and a set of basic conditions to construct new models which can recover Navier–Stokes equations. Besides, the equilibrium function can be easily obtained through a set of equations. By using the platform, we can easily recover the existing models. Some new models are derived from the platform and validated by their application to simulate the two-dimensional driven cavity flow. The obtained numerical results agree very well with available data in the literature.

scholarly journals NUMERICAL SIMULATION OF LID-DRIVEN CAVITY FLOW BY ISOGEOMETRIC ANALYSIS

2021 ◽  
Vol 61 (SI) ◽  
pp. 33-48
Author(s):  
Bohumír Bastl ◽  
Marek Brandner ◽  
Jiří Egermaier ◽  
Hana Horníková ◽  
Kristýna Michálková ◽  
...  
Keyword(s):  
Fluid Flow ◽  
Incompressible Fluid ◽  
Isogeometric Analysis ◽  
Stokes Equations ◽  
Cavity Flow ◽  
Navier Stokes ◽  
Incompressible Fluid Flow ◽  
Navier Stokes Equations ◽  
Flow Solver ◽  
Driven Cavity

In this paper, we present numerical results obtained by an in-house incompressible fluid flow solver based on isogeometric analysis (IgA) for the standard benchmark problem for incompressible fluid flow simulation – lid-driven cavity flow. The steady Navier-Stokes equations are solved in their velocity-pressure formulation and we consider only inf-sup stable pairs of B-spline discretization spaces. The main aim of the paper is to compare the results from our IgA-based flow solver with the results obtained by a standard package based on finite element method with respect to degrees of freedom and stability of the solution. Further, the effectiveness of the recently introduced rIgA method for the steady Navier-Stokes equations is studied.The authors dedicate the paper to Professor K. Kozel on the occasion of his 80th birthday.

scholarly journals A Closed-Form Analytical Solution to the Complete Three-Dimensional Unsteady Compressible Navier-Stokes Equations

2021 ◽  
Author(s):  
Taofiq Amoloye
Keyword(s):  
Reynolds Number ◽  
Numerical Simulations ◽  
Potential Theory ◽  
Stream Function ◽  
Continuity Equation ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Consistent Solution

Abstract The three main approaches in fluid dynamics are actual experiments, numerical simulations, and theoretical solutions. Numerical simulations and theoretical solutions are based on the continuity equation and Navier-Stokes equations (NSE) that govern experimental observations of fluid dynamics.Theoretical solutions can offer huge advantages over numerical solutions and experiments in the understanding of fluid flows and design. These advantages are in terms of cost and time consumption. However, theoretical solutions have been limited by the prized NSE problem that seeks a physically consistent solution than what classical potential theory (CPT) offers. Therefore, the current author refined CPT. He introduced refined potential theory (RPT) that provides a viscous potential/stream function as a physically consistent solution to the NSE problem. This function captures observable unsteady flow features including separation, wake, vortex shedding, compressibility, turbulence, and Reynolds-number-dependence. It appropriately combines the properties of a three-dimensional potential function that satisfy the inertia terms of NSE and the features of a stream function that satisfy the continuity equation, the viscous vorticity equation, and the viscous terms of NSE. RPT has been verified and validated against experimental and numerical results of incompressible unsteady sub-critical Reynolds number flows on stationary finite circular cylinder, sphere, and spheroid.

Comparison of Some Preconditioners for the Incompressible Navier-Stokes Equations

2016 ◽  
Vol 9 (2) ◽  
pp. 239-261 ◽  
Author(s):  
X. He ◽  
C. Vuik
Keyword(s):  
Reynolds Number ◽  
Laminar Flow ◽  
Flat Plate ◽  
Augmented Lagrangian ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Benchmark Problems ◽  
Navier Stokes Equations ◽  
Driven Cavity

AbstractIn this paper we explore the performance of the SIMPLER, augmented Lagrangian, ‘grad-div’ preconditioners and their new variants for the two-by-two block systems arising in the incompressible Navier-Stokes equations. The lid-driven cavity and flow over a finite flat plate are chosen as the benchmark problems. For each problem the Reynolds number varies from a low to the limiting number for a laminar flow.

Sign in / Sign up

Export Citation Format

Share Document