scholarly journals An Alternative HSS Preconditioner for the Unsteady Incompressible Navier-Stokes Equations in Rotation Form

2012 ◽  
Vol 2012 ◽  
pp. 1-12
Author(s):  
Jia Liu
Keyword(s):  
Iterative Method ◽  
Krylov Subspace ◽  
Stokes Equations ◽  
Mesh Size ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Time Step ◽  
Navier Stokes Equations ◽  
Preconditioned Iterative ◽  
Preconditioned Iterative Methods

We study the preconditioned iterative method for the unsteady Navier-Stokes equations. The rotation form of the Oseen system is considered. We apply an efficient preconditioner which is derived from the Hermitian/Skew-Hermitian preconditioner to the Krylov subspace-iterative method. Numerical experiments show the robustness of the preconditioned iterative methods with respect to the mesh size, Reynolds numbers, time step, and algorithm parameters. The preconditioner is efficient and easy to apply for the unsteady Oseen problems in rotation form.

scholarly journals AN ITERATIVE METHOD FOR THE NAVIER-STOKES EQUATIONS IN THE PROBLEM OF A VISCOUS INCOMPRESSIBLE FLUID FLOW AROUND A THIN PLATE

2020 ◽  
pp. 132-142
Author(s):  
M.A. Sumbatyan ◽  
◽  
Ya.A. Berdnik ◽  
A.A. Bondarchuk ◽  
◽  
...  
Keyword(s):  
Integral Equation ◽  
Fluid Flow ◽  
Iterative Method ◽  
Thin Plate ◽  
Stokes Equations ◽  
Reynolds Numbers ◽  
Iteration Step ◽  
Navier Stokes ◽  
Large Reynolds Number ◽  
Navier Stokes Equations

In this paper, the problem on a viscous fluid flow around a thin plate is considered using the exact Navier–Stokes equations. An iterative method is proposed for small velocity perturbations with respect to main flow velocities. At each iterative step, an integral equation is solved for a function of the viscous friction over the plate. The collocation method is used at each iteration step to reduce an integral equation to a system of linear algebraic equations, and the shooting method based on the classical fourth-order Runge-Kutta technique is applied. The solution obtained at each iteration step is compared with the Harrison–Filon solution at low Reynolds numbers, with the classical Blasius solution, and with the results computed using the direct numerical finite-volume method in the ANSYS CFX software for moderate and high Reynolds numbers. The proposed iterative method converges in a few steps. Its accuracy is rather high for small and large Reynolds number, while the error can reach 15% for moderate values.

Flow in a Tube With a Circumferential Wall Cavity

1973 ◽  
Vol 40 (2) ◽  
pp. 355-361 ◽  
Author(s):  
J. F. Stevenson
Keyword(s):  
Stokes Equations ◽  
Separated Flow ◽  
Mesh Size ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Tube Radius ◽  
Cavity Depth ◽  
Navier Stokes Equations ◽  
Flow Through ◽  
Stress Profiles

Streamlines, velocity profiles, and wall shear stress profiles are presented for a numerical solution of the Navier-Stokes equations for steady flow through a tube (radius = 1) with a circumferential wall cavity (depth = 1.33, length = 1.33). For tube Reynolds numbers equal to 0, 50, and 200, the numerical calculations show that a region of separated flow with closed streamlines exists in the cavity and that the attachment points for the separating streamline are located along the cavity wall. An assessment is made of the dependence of the numerical results on mesh size and the type of vorticity boundary condition applied at the protruding corners.

Simulation of Unsteady Flow Around a Cylinder

2015 ◽  
Vol 3 (2) ◽  
pp. 28-49
Author(s):  
Ridha Alwan Ahmed
Keyword(s):  
Stokes Equations ◽  
Lift Coefficient ◽  
Reynolds Numbers ◽  
Mean Value ◽  
Navier Stokes ◽  
Cylinder Surface ◽  
Navier Stokes Equations ◽  
Flow Around A Cylinder ◽  
Numerical Grid ◽  
Good Agreement

       In this paper, the phenomena of vortex shedding from the circular cylinder surface has been studied at several Reynolds Numbers (40≤Re≤ 300).The 2D, unsteady, incompressible, Laminar flow, continuity and Navier Stokes equations have been solved numerically by using CFD Package FLUENT. In this package PISO algorithm is used in the pressure-velocity coupling.        The numerical grid is generated by using Gambit program. The velocity and pressure fields are obtained upstream and downstream of the cylinder at each time and it is also calculated the mean value of drag coefficient and value of lift coefficient .The results showed that the flow is strongly unsteady and unsymmetrical at Re>60. The results have been compared with the available experiments and a good agreement has been found between them

A finite element method for the Navier-Stokes equations in moving domain with application to hemodynamics of the left ventricle

2017 ◽  
Vol 32 (4) ◽  
Author(s):  
Alexander Danilov ◽  
Alexander Lozovskiy ◽  
Maxim Olshanskii ◽  
Yuri Vassilevski
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Left Ventricle ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Time Step ◽  
Navier Stokes Equations ◽  
Computed Tomography Images ◽  
Time Dependent Domain ◽  
Element Method

AbstractThe paper introduces a finite element method for the Navier-Stokes equations of incompressible viscous fluid in a time-dependent domain. The method is based on a quasi-Lagrangian formulation of the problem and handling the geometry in a time-explicit way. We prove that numerical solution satisfies a discrete analogue of the fundamental energy estimate. This stability estimate does not require a CFL time-step restriction. The method is further applied to simulation of a flow in a model of the left ventricle of a human heart, where the ventricle wall dynamics is reconstructed from a sequence of contrast enhanced Computed Tomography images.

Burgers turbulence model for a channel flow

1971 ◽  
Vol 47 (2) ◽  
pp. 321-335 ◽  
Author(s):  
Jon Lee
Keyword(s):  
Channel Flow ◽  
Stokes Equations ◽  
Turbulent Channel Flow ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Amplitude Equations ◽  
Fourier Amplitude ◽  
Navier Stokes Equations ◽  
Burgers Model ◽  
Model Dynamics

The truncated Burgers models have a unique equilibrium state which is defined continuously for all the Reynolds numbers and attainable from a realizable class of initial disturbances. Hence, they represent a sequence of convergent approximations to the original (untruncated) Burgers problem. We have pointed out that consideration of certain degenerate equilibrium states can lead to the successive turbulence-turbulence transitions and finite-jump transitions that were suggested by Case & Chiu. As a prototype of the Navier–Stokes equations, Burgers model can simulate the initial-value type of numerical integration of the Fourier amplitude equations for a turbulent channel flow. Thus, the Burgers model dynamics display certain idiosyncrasies of the actual channel flow problem described by a truncated set of Fourier amplitude equations, which includes only a modest number of modes due to the limited capability of the computer at hand.

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