A comparison of numerical solutions of convective and divergence forms of the Navier-Stokes equations for the driven cavity problem

1981 ◽  
Vol 43 (2) ◽  
pp. 260-267 ◽  
Author(s):  
Murli M Gupta
Keyword(s):  
Numerical Solutions ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Driven Cavity

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.

A numerical study of the interaction between unsteay free-stream disturbances and localized variations in surface geometry

1989 ◽  
Vol 209 ◽  
pp. 285-308 ◽  
Author(s):  
R. J. Bodonyi ◽  
W. J. C. Welch ◽  
P. W. Duck ◽  
M. Tadjfar
Keyword(s):  
Numerical Solutions ◽  
Free Stream ◽  
Stokes Equations ◽  
Numerical Study ◽  
Navier Stokes ◽  
Surface Geometry ◽  
Navier Stokes Equations ◽  
S Waves ◽  
Tollmien Schlichting

A numerical study of the generation of Tollmien-Schlichting (T–S) waves due to the interaction between a small free-stream disturbance and a small localized variation of the surface geometry has been carried out using both finite–difference and spectral methods. The nonlinear steady flow is of the viscous–inviscid interactive type while the unsteady disturbed flow is assumed to be governed by the Navier–Stokes equations linearized about this flow. Numerical solutions illustrate the growth or decay of the T–S waves generated by the interaction between the free-stream disturbance and the surface distortion, depending on the value of the scaled Strouhal number. An important result of this receptivity problem is the numerical determination of the amplitude of the T–S waves.

NUMERICAL SOLUTIONS OF 2D AND 3D SLAMMING PROBLEMS

2021 ◽  
Vol 153 (A2) ◽  
Author(s):  
Q Yang ◽  
W Qiu
Keyword(s):  
Free Surface ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Type Equation ◽  
The Body ◽  
Navier Stokes ◽  
Time Step ◽  
Navier Stokes Equations ◽  
Highly Nonlinear ◽  
2D And 3D

Slamming forces on 2D and 3D bodies have been computed based on a CIP method. The highly nonlinear water entry problem governed by the Navier-Stokes equations was solved by a CIP based finite difference method on a fixed Cartesian grid. In the computation, a compact upwind scheme was employed for the advection calculations and a pressure-based algorithm was applied to treat the multiple phases. The free surface and the body boundaries were captured using density functions. For the pressure calculation, a Poisson-type equation was solved at each time step by the conjugate gradient iterative method. Validation studies were carried out for 2D wedges with various deadrise angles ranging from 0 to 60 degrees at constant vertical velocity. In the cases of wedges with small deadrise angles, the compressibility of air between the bottom of the wedge and the free surface was modelled. Studies were also extended to 3D bodies, such as a sphere, a cylinder and a catamaran, entering calm water. Computed pressures, free surface elevations and hydrodynamic forces were compared with experimental data and the numerical solutions by other methods.

Implementation of a Semi-Implicit Pressure-Based Multigrid Fluid Flow Algorithm on a Graphics Processing Unit

2009 ◽  
Author(s):  
Aaron F. Shinn ◽  
S. P. Vanka
Keyword(s):  
Stokes Equations ◽  
Graphics Processing Unit ◽  
Navier Stokes ◽  
Processing Unit ◽  
Navier Stokes Equations ◽  
Driven Cavity ◽  
Multigrid Algorithm ◽  
Computational Speed ◽  
Speed Up ◽  
Graphics Processing

A semi-implicit pressure based multigrid algorithm for solving the incompressible Navier-Stokes equations was implemented on a Graphics Processing Unit (GPU) using CUDA (Compute Unified Device Architecture). The multigrid method employed was the Full Approximation Scheme (FAS), which is used for solving nonlinear equations. This algorithm is applied to the 2D driven cavity problem and compared to the CPU version of the code (written in Fortran) to assess computational speed-up.

scholarly journals On the Importance of the Influence of both Velocity and Aspect Ratios on the Occurrence of Bifurcation Phenomena within a Two-Sided Lid-Driven Enclosure

2015 ◽  
Vol 55 ◽  
pp. 160-172
Author(s):  
Fayçal Hammami ◽  
Nader Ben Cheikh ◽  
Brahim Ben Beya
Keyword(s):  
Stokes Equations ◽  
Numerical Study ◽  
Numerical Results ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Left Wall ◽  
Driven Cavity ◽  
Aspect Ratios ◽  
The Stability ◽  
The Right

This paper deals with the numerical study of bifurcations in a two-sided lid driven cavity flow. The flow is generated by moving the upper wall to the right while moving the left wall downwards. Numerical simulations are performed by solving the unsteady two dimensional Navier-Stokes equations using the finite volume method and multigrid acceleration. In this problem, the ratio of the height to the width of the cavity are ranged from H/L = 0.25 to 1.5. The code for this cavity is presented using rectangular cavity with the grids 144 × 36, 144 × 72, 144 × 104, 144 × 136, 144 × 176 and 144 × 216. Numerous comparisons with the results available in the literature are given. Very good agreements are found between current numerical results and published numerical results. Various velocity ratios ranged in 0.01≤ α ≤ 0.99 at a fixed aspect ratios (A = 0.5, 0.75, 1.25 and 1.5) were considered. It is observed that the transition to the unsteady regime follows the classical scheme of a Hopf bifurcation. The stability analysis depending on the aspect ratio, velocity ratios α and the Reynolds number when transition phenomenon occurs is considered in this paper.

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 Mathematical Model for the Electrokinetic Instability of Electrolyte Flow

2019 ◽  
Vol 224 ◽  
pp. 02003
Author(s):  
Andrey Shobukhov
Keyword(s):  
Electric Potential ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Fluid Velocity ◽  
Steady State Solution ◽  
Stability Loss ◽  
Navier Stokes ◽  
Ion Distribution ◽  
Navier Stokes Equations ◽  
Dilute Aqueous Solution

We study a one-dimensional model of the dilute aqueous solution of KCl in the electric field. Our model is based on a set of Nernst-Planck-Poisson equations and includes the incompressible fluid velocity as a parameter. We demonstrate instability of the linear electric potential variation for the uniform ion distribution and compare analytical results with numerical solutions. The developed model successfully describes the stability loss of the steady state solution and demonstrates the emerging of spatially non-uniform distribution of the electric potential. However, this model should be generalized by accounting for the convective movement via the addition of the Navier-Stokes equations in order to substantially extend its application field.

A Simplified Parallel Two-Level Iterative Method for Simulation of Incompressible Navier-Stokes Equations

2015 ◽  
Vol 7 (6) ◽  
pp. 715-735
Author(s):  
Yueqiang Shang ◽  
Jin Qin
Keyword(s):  
Stokes Equations ◽  
Stokes Problem ◽  
Coarse Grid ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Driven Cavity ◽  
Step Flow ◽  
Grid Solution ◽  
Oseen Problem ◽  
Parallel Iterative

AbstractBased on two-grid discretization, a simplified parallel iterative finite element method for the simulation of incompressible Navier-Stokes equations is developed and analyzed. The method is based on a fixed point iteration for the equations on a coarse grid, where a Stokes problem is solved at each iteration. Then, on overlapped local fine grids, corrections are calculated in parallel by solving an Oseen problem in which the fixed convection is given by the coarse grid solution. Error bounds of the approximate solution are derived. Numerical results on examples of known analytical solutions, lid-driven cavity flow and backward-facing step flow are also given to demonstrate the effectiveness of the method.

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