Navier–Stokes Equations with Nonhomogeneous Boundary Conditions in a Bounded Three-Dimensional Domain

2010 ◽  
Vol 13 (3) ◽  
pp. 309-339 ◽  
Author(s):  
Vincent Girinon
Keyword(s):  
Boundary Conditions ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Nonhomogeneous Boundary ◽  
Nonhomogeneous Boundary Conditions ◽  
Dimensional Domain

Attractors for the modifications of the three-dimensional Navier-Stokes equations

1994 ◽  
Vol 346 (1679) ◽  
pp. 173-190 ◽  
Keyword(s):  
Viscous Fluid ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Fluid Flows ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Initial Boundary Value ◽  
Dimensional Domain

The modifications of the three-dimensional Navier-Stokes equations, which I suggested earlier for the description of viscous fluid flows with large gradients of velocities, are considered. It is proved that the first initial-boundary value problem for these equations in any bounded three-dimensional domain has a compact minimal global B-attractor. Some properties of the attractor are established.

Analysis of a Navier–Stokes–Darcy coupling problem

2016 ◽  
Vol 7 (3) ◽  
Author(s):  
Yassine Mabrouki ◽  
Jamil Satouri
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Standard Condition ◽  
Navier Stokes ◽  
Existence Of A Solution ◽  
Navier Stokes Equations ◽  
Coupling Problem ◽  
Coupled Problem ◽  
Darcy Equations ◽  
Dimensional Domain

AbstractThe aim of this work is to present a model for coupling the Darcy equations in a porous medium with the Navier–Stokes equations in the cracks. We consider a two- or three-dimensional domain with non-standard condition at the interface, namely the continuity of the pressure. We propose a mixed formulation and establish the existence of a solution for the coupled problem.

Computation of Inviscid Incompressible Flow Using the Primitive Variable Formulation

1986 ◽  
Vol 108 (1) ◽  
pp. 68-75 ◽  
Author(s):  
S. Abdallah ◽  
H. G. Smith
Keyword(s):  
Boundary Conditions ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Type Equation ◽  
Momentum Equation ◽  
Navier Stokes ◽  
Fine Grid ◽  
Navier Stokes Equations ◽  
Pressure Poisson Equation ◽  
Fine Mesh

The primitive variable formulation originally developed for the incompressible Navier–Stokes equations is applied for the solution of the incompressible Euler equations. The unsteady momentum equation is solved for the velocity field and the continuity equation is satisfied indirectly in a Poisson-type equation for the pressure (divergence of the momentum equation). Solutions for the pressure Poisson equation with derivative boundary conditions exist only if a compatibility condition is satisfied (Green’s theorem). This condition is not automatically satisfied on nonstaggered grids. A new method for the solution of the pressure equation with derivative boundary conditions on a nonstaggered grid [25] is used here for the calculation of the pressure. Three-dimensional solutions for the inviscid rotational flow in a 90 deg curved duct are obtained on a very fine mesh (17 × 17 × 29). The use of a fine grid mesh allows for the accurate prediction of the development of the secondary flow. The computed results are in good agreement with the experimental data of Joy [15].

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