Sharp Existence Results¶for the Stationary Navier-Stokes Problem¶in Three-Dimensional Exterior Domains

2000 ◽  
Vol 154 (4) ◽  
pp. 343-368 ◽  
Author(s):  
Giovanni P. Galdi ◽  
Patrick J. Rabier
Keyword(s):  
Stokes Problem ◽  
Three Dimensional ◽  
Existence Results ◽  
Navier Stokes ◽  
Exterior Domains

scholarly journals ON COUPLED PROBLEMS FOR VISCOUS FLOW IN EXTERIOR DOMAINS

1998 ◽  
Vol 08 (04) ◽  
pp. 657-684 ◽  
Author(s):  
M. FEISTAUER ◽  
C. SCHWAB
Keyword(s):  
Stokes Flow ◽  
Stokes System ◽  
Stokes Problem ◽  
Large Data ◽  
Transmission Conditions ◽  
Navier Stokes ◽  
Coupled Problems ◽  
Exterior Domains ◽  
Existence Of A Solution ◽  
Coupled Problem

The use of the complete Navier–Stokes system in an unbounded domain is not always convenient in computations and, therefore, the Navier–Stokes problem is often truncated to a bounded domain. In this paper we simulate the interaction between the flow in this domain and the exterior flow with the aid of a coupled problem. We propose in particular a linear approximation of the exterior flow (here the Stokes flow or potential flow) coupled with the interior Navier–Stokes problem via suitable transmission conditions on the artificial interface between the interior and exterior domains. Our choice of the transmission conditions ensures the existence of a solution of the coupled problem, also for large data.

On the stationary Navier–Stokes problem in 3D exterior domains

2018 ◽  
Vol 99 (9) ◽  
pp. 1485-1506
Author(s):  
Vincenzo Coscia ◽  
Remigio Russo ◽  
Alfonsina Tartaglione
Keyword(s):  
Stokes Problem ◽  
Navier Stokes ◽  
Exterior Domains

scholarly journals A 3D Chebyshev-Fourier algorithm for convection equations in low Mach number approximation

2009 ◽  
pp. 607-625
Author(s):  
Ouafa Bouloumou ◽  
Eric Serre ◽  
Jochen Fröhlich
Keyword(s):  
Mach Number ◽  
Stokes Equations ◽  
Stokes Problem ◽  
Three Dimensional ◽  
Time Discretization ◽  
Navier Stokes ◽  
Working Fluid ◽  
Uzawa Algorithm ◽  
Low Mach Number ◽  
Preconditioned Iterative

A three-dimensional spectral method based on Chebyshev-Chebyshev-Fourier discretizations is presented in the framework of the low Mach number approximation of Navier-Stokes equations. The working fluid is assumed to be a perfect gas with constant thermodynamic properties. The generalized Stokes problem, which arises from the time discretization by a second-order semi-implicit scheme, is solved by a preconditioned iterative Uzawa algorithm. Several validation results are presented in the case of steady and unsteady flows. This model is also evaluated for natural convection flows with large density variations in the case of a tall differentially heated cavity of aspect ratio 8. It is found that on contrary to convection at small temperature differences (Boussinesq), the 2D unsteady solution at Ra = 3.4 x 105 is unstable to 3D perturbations.

scholarly journals Linear stability analysis of capillary instabilities for concentric cylindrical shells

2011 ◽  
Vol 683 ◽  
pp. 235-262 ◽  
Author(s):  
X. Liang ◽  
D. S. Deng ◽  
J.-C. Nave ◽  
Steven G. Johnson
Keyword(s):  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Layer Structure ◽  
Stokes Problem ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Flow Simulations ◽  
Growth Modes ◽  
Capillary Instabilities

AbstractMotivated by complex multi-fluid geometries currently being explored in fibre-device manufacturing, we study capillary instabilities in concentric cylindrical flows of $N$ fluids with arbitrary viscosities, thicknesses, densities, and surface tensions in both the Stokes regime and for the full Navier–Stokes problem. Generalizing previous work by Tomotika ($N= 2$), Stone & Brenner ($N= 3$, equal viscosities) and others, we present a full linear stability analysis of the growth modes and rates, reducing the system to a linear generalized eigenproblem in the Stokes case. Furthermore, we demonstrate by Plateau-style geometrical arguments that only axisymmetric instabilities need be considered. We show that the $N= 3$ case is already sufficient to obtain several interesting phenomena: limiting cases of thin shells or low shell viscosity that reduce to $N= 2$ problems, and a system with competing breakup processes at very different length scales. The latter is demonstrated with full three-dimensional Stokes-flow simulations. Many $N\gt 3$ cases remain to be explored, and as a first step we discuss two illustrative $N\ensuremath{\rightarrow} \infty $ cases, an alternating-layer structure and a geometry with a continuously varying viscosity.

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