The Newton-Raphson approximation applied to the Navier-Stokes equations with application to the base flow problem

1968 ◽  
Vol 48 (1) ◽  
pp. 1-9 ◽  
Author(s):  
I. L. Parmet ◽  
E. Saibel
Keyword(s):  
Flow Problem ◽  
Stokes Equations ◽  
Base Flow ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Newton Raphson

scholarly journals Numerical stability analysis of a vortex ring with swirl

2019 ◽  
Vol 878 ◽  
pp. 5-36 ◽  
Author(s):  
Yuji Hattori ◽  
Francisco J. Blanco-Rodríguez ◽  
Stéphane Le Dizès
Keyword(s):  
Numerical Simulation ◽  
Growth Rate ◽  
Direct Numerical Simulation ◽  
Vortex Ring ◽  
Stokes Equations ◽  
Base Flow ◽  
Critical Layer ◽  
Navier Stokes ◽  
Instability Mode ◽  
Navier Stokes Equations

The linear instability of a vortex ring with swirl with Gaussian distributions of azimuthal vorticity and velocity in its core is studied by direct numerical simulation. The numerical study is carried out in two steps: first, an axisymmetric simulation of the Navier–Stokes equations is performed to obtain the quasi-steady state that forms a base flow; then, the equations are linearized around this base flow and integrated for a sufficiently long time to obtain the characteristics of the most unstable mode. It is shown that the vortex rings are subjected to curvature instability as predicted analytically by Blanco-Rodríguez & Le Dizès (J. Fluid Mech., vol. 814, 2017, pp. 397–415). Both the structure and the growth rate of the unstable modes obtained numerically are in good agreement with the analytical results. However, a small overestimation (e.g. 22 % for a curvature instability mode) by the theory of the numerical growth rate is found for some instability modes. This is most likely due to evaluation of the critical layer damping which is performed for the waves on axisymmetric line vortices in the analysis. The actual position of the critical layer is affected by deformation of the core due to the curvature effect; as a result, the damping rate changes since it is sensitive to the position of the critical layer. Competition between the curvature and elliptic instabilities is also investigated. Without swirl, only the elliptic instability is observed in agreement with previous numerical and experimental results. In the presence of swirl, sharp bands of both curvature and elliptic instabilities are obtained for $\unicode[STIX]{x1D700}=a/R=0.1$, where $a$ is the vortex core radius and $R$ the ring radius, while the elliptic instability dominates for $\unicode[STIX]{x1D700}=0.18$. New types of instability mode are also obtained: a special curvature mode composed of three waves is observed and spiral modes that do not seem to be related to any wave resonance. The curvature instability is also confirmed by direct numerical simulation of the full Navier–Stokes equations. Weakly nonlinear saturation and subsequent decay of the curvature instability are also observed.

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.

Directivity and intermittency in the nearfield of a Mach 1.3 jet

2017 ◽  
Vol 16 (3) ◽  
pp. 135-164 ◽  
Author(s):  
S Unnikrishnan ◽  
Datta V Gaitonde ◽  
Lionel Agostini
Keyword(s):  
Acoustic Field ◽  
Stokes Equations ◽  
Base Flow ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Local Fluctuations ◽  
Mode Decomposition ◽  
Gradual Evolution ◽  
Large Eddy ◽  
High Frequency Content

Local fluctuations in a Mach 1.3 cold jet are tracked to understand the genesis of nearfield directivity and intermittency. A newly developed approach leveraging two synchronized large-eddy simulations is employed to solve the forced Navier–Stokes equations, linearized about the evolving unsteady base flow. The results are summarized by exposing the effect of two acoustically significant turbulent regions: the lip-line and core collapse location. The near-acoustic field displays the clear signature of the two regions. However, for both regions, the nearfield evolution of the perturbation field is characterized by generation of intermittent wavepackets, which propagate into the near-acoustic field and gradually acquire their expected broadband and narrowband characteristics at sideline and downstream angles respectively. The simulations elucidate how higher frequencies are obtained in the sideline directions as lower frequencies are filtered out of the forcing fluctuations. Likewise, shallow-angle acoustic signals arise through filtering of high frequency content in that direction. The directivity and intermittency are connected to the filtering of scales by jet turbulence with empirical mode decomposition. The observations highlight the gradual evolution of seemingly random core turbulence into well-defined intermittent wavepackets in the nearfield of the jet. The manner in which centerline fluctuations are segregated into upstream, sideline, and downstream components is examined through narrowband correlations. A similar analysis for the lipline contribution shows primarily upstream and downstream patterns because of the larger structures in the shear layer.

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.

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

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.

scholarly journals Optimization of artillery projectiles base drag reduction using hot base flow

2019 ◽  
Vol 23 (1) ◽  
pp. 353-364
Author(s):  
Mohammed Dali ◽  
Slobodan Jaramaz
Keyword(s):  
Drag Reduction ◽  
Stokes Equations ◽  
Flow Characteristics ◽  
Turbulence Models ◽  
Combustion Products ◽  
Base Flow ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Base Bleed ◽  
Base Drag

The CFD numerical simulations were carried out to investigate the base drag characteristics of a projectile with base bleed unit with a central jet. Different base bleed grain types with different combustion temperatures were used. The goal was to find a way to effectively control the base flow for base drag reduction and optimisate the latter using an adequate CFD software. Axisymmetric, compressible, mass-averaged Navier-Stokes equations are solved using the k-? SST, transition k-kl-?, and RSM turbulence models. The various base flow characteristics are obtained by the change in the non-dimensionalized injection impulse. The results obtained through the present study show that there is an optimum bleed condition for all base bleed grains tested. That optimum is dependent on the temperature of the grain combustion products. The optimum reduces the total drag for 6,9% in the case of air injection at temperature of 300 K and reaches up to 28% in the case of propellant combustion products injection at almost 2500 K. Besides, the increasing of molecular weight has a role no less important than temperature of the combustion products in terms of base drag reduction.

Sign in / Sign up

Export Citation Format

Share Document