A shear flow problem for the compressible Navier-Stokes equations

1998 ◽  
Vol 33 (2) ◽  
pp. 247-257 ◽  
Author(s):  
V.V. Shelukhin
Keyword(s):  
Shear Flow ◽  
Flow Problem ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations

scholarly journals Disconnected stationary solutions for 3D Kolmogorov flow problem: preliminary results

2021 ◽  
Vol 2090 (1) ◽  
pp. 012046
Author(s):  
Nikolay M. Evstigneev
Keyword(s):  
Flow Problem ◽  
Stokes Equations ◽  
Continuation Method ◽  
Fourier Method ◽  
Stationary Solutions ◽  
Navier Stokes ◽  
System Of Nonlinear Equations ◽  
Arc Length ◽  
Navier Stokes Equations ◽  
Numerical Bifurcation

Abstract The extension of the classical A.N. Kolmogorov’s flow problem for the stationary 3D Navier-Stokes equations on a stretched torus for velocity vector function is considered. A spectral Fourier method with the Leray projection is used to solve the problem numerically. The resulting system of nonlinear equations is used to perform numerical bifurcation analysis. The problem is analyzed by constructing solution curves in the parameter-phase space using previously developed deflated pseudo arc-length continuation method. Disconnected solutions from the main solution branch are found. These results are preliminary and shall be generalized elsewhere.

scholarly journals In-Flow and Out-Flow Problem for the Stokes System

2020 ◽  
Vol 22 (4) ◽  
Author(s):  
Bernard Nowakowski ◽  
Gerhard Ströhmer
Keyword(s):  
Stokes System ◽  
Flow Problem ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Tangential Component ◽  
Regularity Of Solutions ◽  
Navier Stokes ◽  
Lateral Part ◽  
Navier Stokes Equations ◽  
Stationary Navier Stokes Equations

AbstractWe investigate the existence and regularity of solutions to the stationary Stokes system and non-stationary Navier–Stokes equations in three dimensional bounded domains with in- and out-lets. We assume that on the in- and out-flow parts of the boundary the pressure is prescribed and the tangential component of the velocity field is zero, whereas on the lateral part of the boundary the fluid is at rest.

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.

Lift, drag and added mass of a hemispherical bubble sliding and growing on a wall in a viscous linear shear flow

2008 ◽  
Vol 366 (1873) ◽  
pp. 2233-2248 ◽  
Author(s):  
Dominique Legendre ◽  
Catherine Colin ◽  
Typhaine Coquard
Keyword(s):  
Shear Flow ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Added Mass ◽  
Unsteady Motion ◽  
Navier Stokes ◽  
Mass Force ◽  
Navier Stokes Equations ◽  
Wide Range ◽  
Linear Shear

The three-dimensional flow around a hemispherical bubble sliding and growing on a wall in a viscous linear shear flow is studied numerically by solving the full Navier–Stokes equations in a boundary-fitted domain. The main goal of the present study is to provide a complete description of the forces experienced by the bubble (drag, lift and added mass) over a wide range of sliding and shear Reynolds numbers (0.01≤ Re b , Re α ≤2000) and shear rate (0≤ Sr ≤5). The drag and lift forces are computed successively for the following situations: an immobile bubble in a linear shear flow; a bubble sliding on the wall in a fluid at rest; and a bubble sliding in a linear shear flow. The added-mass force is studied by considering an unsteady motion relative to the wall or a time-dependent radius.

scholarly journals Solution of Navier-Stokes equations for fluids with magnetorheological compensation used in structures with energy dissipaters

2022 ◽  
Vol 2159 (1) ◽  
pp. 012007
Author(s):  
N Balaguera Medina ◽  
M A Atuesta ◽  
O A Nieto ◽  
P A Ospina Henao
Keyword(s):  
Flow Problem ◽  
Stokes Equations ◽  
Rectangular Cavity ◽  
Navier Stokes ◽  
Computational Fluid Mechanics ◽  
Civil Structures ◽  
Navier Stokes Equations ◽  
Shock Absorbers ◽  
Classic Problem ◽  
Energy Dissipators

Abstract The fixed-wall rectangular cavity flow problem is a classic problem that has been studied since the beginning of computational fluid mechanics. The present work aims to provide a numerical and computational solution of the Navier-Stokes equations using the finite difference method, applied to model the problem of a magnetorheological fluid in a rectangular cavity with a fixed wall in shock absorbers devices, used in civil structures that use energy dissipators.

Computations of Ship Stern and Wake Flow and Comparisons with Experiment

1990 ◽  
Vol 34 (03) ◽  
pp. 179-193
Author(s):  
V. C. Patel ◽  
H. C. Chen ◽  
S. Ju
Keyword(s):  
Experimental Data ◽  
Shear Flow ◽  
Numerical Method ◽  
Stokes Equations ◽  
Ship Hull ◽  
Wake Flow ◽  
Navier Stokes ◽  
Turbulent Shear ◽  
Turbulent Shear Flow ◽  
Navier Stokes Equations

A numerical method for the solution of the Reynolds-averaged Navier-Stokes equations has been employed to study the turbulent shear flow over the stern and in the wake of a ship hull. Detailed comparisons are made between the numerical results and available experimental data to show that most of the important overall features of such flows can now be predicted with considerable accuracy.

scholarly journals Analytic and Numerical Solutions of Couette Flow Problem: A Comparative Study

2017 ◽  
Vol 12 (1) ◽  
pp. 105-113
Author(s):  
Dhak Bahadur Thapa ◽  
Kedar Nath Uprety
Keyword(s):  
Differential Equation ◽  
Couette Flow ◽  
Numerical Solutions ◽  
Flow Problem ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Parabolic Partial Differential Equation ◽  
Navier Stokes Equations ◽  
One Dimensional ◽  
Nicolson Scheme

In this work, an incompressible viscous Couette flow is derived by simplifying the Navier-Stokes equations and the resulting one dimensional linear parabolic partial differential equation is solved numerically employing a second order finit difference Crank-Nicolson scheme. The numerical solution and the exact solution are presented graphically.Journal of the Institute of Engineering, 2016, 12(1): 105-113

The evolution of thermocline waves from an oscillatory disturbance

1993 ◽  
Vol 254 ◽  
pp. 401-416 ◽  
Author(s):  
D. Nicolaou ◽  
R. Liu ◽  
T. N. Stevenson
Keyword(s):  
Finite Difference ◽  
Shear Flow ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Ray Theory ◽  
Navier Stokes Equations ◽  
Linear Shear ◽  
Wave Shapes ◽  
The Way

The way in which energy propagates away from a two-dimensional oscillatory disturbance in a thermocline is considered theoretically and experimentally. It is shown how the St. Andrew's-cross-wave is modified by reflections and how the cross-wave can develop into thermocline waves. A linear shear flow is then superimposed on the thermocline. Ray theory is used to evaluate the wave shapes and these are compared to finite-difference solutions of the full Navier–Stokes equations.

scholarly journals EXISTENCE AND UNIQUENESS OF STRONG SOLUTIONS FOR A COMPRESSIBLE MULTIPHASE NAVIER–STOKES MISCIBLE FLUID-FLOW PROBLEM IN DIMENSION n = 1

2009 ◽  
Vol 19 (03) ◽  
pp. 443-476 ◽  
Author(s):  
C. MICHOSKI ◽  
A. VASSEUR
Keyword(s):  
Diffusion Coefficient ◽  
Fluid Flow ◽  
Existence And Uniqueness ◽  
Flow Problem ◽  
Stokes Equations ◽  
Strong Solutions ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Global Existence And Uniqueness ◽  
Miscible Fluid

We prove the global existence and uniqueness of strong solutions for a compressible multifluid described by the barotropic Navier–Stokes equations in dim = 1. The result holds when the diffusion coefficient depends on the pressure. It relies on a global control in time of the L2 norm of the space derivative of the density, via a new kind of entropy.

Bounds for turbulent shear flow

1970 ◽  
Vol 41 (1) ◽  
pp. 219-240 ◽  
Author(s):  
F. H. Busse
Keyword(s):  
Shear Flow ◽  
Turbulent Flow ◽  
Stokes Equations ◽  
Equations Of Motion ◽  
Variational Problems ◽  
Navier Stokes ◽  
Turbulent Shear ◽  
Turbulent Shear Flow ◽  
Navier Stokes Equations ◽  
Experimental Values

Bounds on the transport of momentum in turbulent shear flow are derived by variational methods. In particular, variational problems for the turbulent regimes of plane Couette flow, channel flow, and pipe flow are considered. The Euler equations resemble the basic Navier–Stokes equations of motion in many respects and may serve as model equations for turbulence. Moreover, the comparison of the upper bound with the experimental values of turbulent momentum transport shows a rather close similarity. The same fact holds with respect to other properties when the observed turbulent flow is compared with the structure of the extremalizing solution of the variational problem. It is suggested that the instability of the sublayer adjacent to the walls is responsible for the tendency of the physically realized turbulent flow to approach the properties of the extremalizing vector field.

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