scholarly journals Large Eddy Simulation of Laminar and Turbulent Flow on Collocated and Staggered Grids

2011 ◽  
Vol 2011 ◽  
pp. 1-13 ◽  
Author(s):  
M. J. Ketabdari ◽  
H. Saghi
Keyword(s):  
Stokes Equations ◽  
Solution Procedure ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Staggered Grids ◽  
Driven Cavity ◽  
Eddy Simulation ◽  
Laminar And Turbulent Flow ◽  
Basic Equations ◽  
Collocated Grids

Momentum and Continuity are the basic equations for fluid flow modeling. The momentum equations in their final form are known as Navier-Stokes equations and can be solved using different numerical methods. There are several approaches such as SIMPLE, PISO, and Fractional Step for solving these equations. In solution procedure, it needs to decide where to store the velocity components. Staggered and Collocated grids can be used to evaluate this problem. On Staggered grids, the velocity components are stored at the cell face, and the scalar variables such as pressure are stored at the central nodes. However, on Collocated grids, all parameters are defined at the same location at the central nodes. The Staggered grids method gives more accurate pressure gradient estimation. However, Collocated grids method is simpler for solving the equations. In this paper, for solving Navier-Stokes equations, Collocated and Staggered grids are employed. Comparison of horizontal and vertical velocities and stream lines at various Reynolds numbers was performed. The results were validated using standard tests such as lid-driven cavity, channel and backward facing step. Discussion is made on accuracy of these methods to estimate horizontal and vertical velocity profiles.

Detached-Eddy Simulations Over a Simplified Landing Gear

2002 ◽  
Vol 124 (2) ◽  
pp. 413-423 ◽  
Author(s):  
L. S. Hedges ◽  
A. K. Travin ◽  
P. R. Spalart
Keyword(s):  
Stokes Equations ◽  
Separated Flow ◽  
Flow Fields ◽  
Equation Model ◽  
Landing Gear ◽  
Navier Stokes ◽  
Detached Eddy Simulation ◽  
Navier Stokes Equations ◽  
Instantaneous Flow ◽  
Eddy Simulation

The flow around a generic airliner landing-gear truck is calculated using the methods of Detached-Eddy Simulation, and of Unsteady Reynolds-Averaged Navier-Stokes Equations, with the Spalart-Allmaras one-equation model. The two simulations have identical numerics, using a multi-block structured grid with about 2.5 million points. The Reynolds number is 6×105. Comparison to the experiment of Lazos shows that the simulations predict the pressure on the wheels accurately for such a massively separated flow with strong interference. DES performs somewhat better than URANS. Drag and lift are not predicted as well. The time-averaged and instantaneous flow fields are studied, particularly to determine their suitability for the physics-based prediction of noise. The two time-averaged flow fields are similar, though the DES shows more turbulence intensity overall. The instantaneous flow fields are very dissimilar. DES develops a much wider range of unsteady scales of motion and appears promising for noise prediction, up to some frequency limit.

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.

A Cartesian Explicit Solver for Complex Hydrodynamic Applications

2014 ◽  
Author(s):  
P. Bigay ◽  
A. Bardin ◽  
G. Oger ◽  
D. Le Touzé
Keyword(s):  
Level Set ◽  
Incompressible Flows ◽  
Stokes Equations ◽  
Simulation Method ◽  
Navier Stokes ◽  
Viscous Effects ◽  
Navier Stokes Equations ◽  
Eddy Simulation ◽  
Flow Past A Cylinder ◽  
Explicit Solver

In order to efficiently address complex problems in hydrodynamics, the advances in the development of a new method are presented here. This method aims at finding a good compromise between computational efficiency, accuracy, and easy handling of complex geometries. The chosen method is an Explicit Cartesian Finite Volume method for Hydrodynamics (ECFVH) based on a compressible (hyperbolic) solver, with a ghost-cell method for geometry handling and a Level-set method for the treatment of biphase-flows. The explicit nature of the solver is obtained through a weakly-compressible approach chosen to simulate nearly-incompressible flows. The explicit cell-centered resolution allows for an efficient solving of very large simulations together with a straightforward handling of multi-physics. A characteristic flux method for solving the hyperbolic part of the Navier-Stokes equations is used. The treatment of arbitrary geometries is addressed in the hyperbolic and viscous framework. Viscous effects are computed via a finite difference computation of viscous fluxes and turbulent effects are addressed via a Large-Eddy Simulation method (LES). The Level-Set solver used to handle biphase flows is also presented. The solver is validated on 2-D test cases (flow past a cylinder, 2-D dam break) and future improvements are discussed.

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.

Fekete-Gauss Spectral Elements for Incompressible Navier-Stokes Flows: The Two-Dimensional Case

2013 ◽  
Vol 13 (5) ◽  
pp. 1309-1329 ◽  
Author(s):  
Laura Lazar ◽  
Richard Pasquetti ◽  
Francesca Rapetti
Keyword(s):  
Degrees Of Freedom ◽  
Stokes Equations ◽  
Schur Complement ◽  
Spectral Element ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Driven Cavity ◽  
Flow Past A Cylinder ◽  
Accuracy Study

AbstractSpectral element methods on simplicial meshes, say TSEM, show both the advantages of spectral and finite element methods, i.e., spectral accuracy and geometrical flexibility. We present aTSEM solver of the two-dimensional (2D) incompressible Navier-Stokes equations, with possible extension to the 3D case. It uses a projection method in time and piecewise polynomial basis functions of arbitrary degree in space. The so-called Fekete-Gauss TSEM is employed,i.e., Fekete (resp. Gauss) points of the triangle are used as interpolation (resp. quadrature) points. For the sake of consistency, isoparametric elements are used to approximate curved geometries. The resolution algorithm is based on an efficient Schur complement method, so that one only solves for the element boundary nodes. Moreover, the algebraic system is never assembled, therefore the number of degrees of freedom is not limiting. An accuracy study is carried out and results are provided for classical benchmarks: the driven cavity flow, the flow between eccentric cylinders and the flow past a cylinder.

scholarly journals The use of dual reciprocity method for 2D laminar viscous flow

2020 ◽  
Vol 310 ◽  
pp. 00044
Author(s):  
Juraj Mužík
Keyword(s):  
Viscous Flow ◽  
Flow Problem ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Singular Boundary ◽  
Navier Stokes Equations ◽  
Driven Cavity ◽  
Boundary Method ◽  
2D Flow ◽  
Singular Boundary Method

The paper presents the use of the dual reciprocity multidomain singular boundary method (SBMDR) for the solution of the laminar viscous flow problem described by Navier-Stokes equations. A homogeneous part of the solution is solved using a singular boundary method with the 2D Stokes fundamental solution - Stokeslet. The dual reciprocity approach has been chosen because it is ideal for the treatment of the nonhomogeneous and nonlinear terms of Navier-Stokes equations. The presented SBMDR approach to the solution of the 2D flow problem is demonstrated on a standard benchmark problem - lid-driven cavity.

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