A new scheme for the incompressible Navier-Stokes equations employing alternating-direction operator splitting and domain decomposition

1998 ◽  
Author(s):  
John Spyropoulos ◽  
Jim Douglas, Jr. ◽  
A. Lyrintzis
Keyword(s):  
Domain Decomposition ◽  
Stokes Equations ◽  
Operator Splitting ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Alternating Direction

A FICTITIOUS DOMAIN / DOMAIN DECOMPOSITION METHOD AND ITS APPLICATIONS

2005 ◽  
Vol 19 (28n29) ◽  
pp. 1523-1526
Author(s):  
CHUNHUA ZHOU ◽  
YONGFENG YAO
Keyword(s):  
Domain Decomposition ◽  
Variational Formulation ◽  
Decomposition Method ◽  
Stokes Equations ◽  
Domain Decomposition Method ◽  
Operator Splitting ◽  
Time Discretization ◽  
Navier Stokes ◽  
Fictitious Domain ◽  
Navier Stokes Equations

In this article, the combination of fictitious domain and domain decomposition has been presented. First, we construct an equivalent variational formulation for the Dirichlet problem of linear elliptic operators and discuss the space approximation. Then the approach is applied to the incompressible Navier-Stokes equations, including construction of the variational formulation and time discretization by operator splitting. Finally, some numerical results are presented to validate our approach.

Flow in Cavities With Curved Boundaries

2009 ◽  
Author(s):  
Guillermo E. Ovando ◽  
Juan C. Prince ◽  
Sandy L. Ovando
Keyword(s):  
Stokes Equations ◽  
Operator Splitting ◽  
Vortex Formation ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
The Finite Element Method ◽  
Curved Boundaries ◽  
Navier Stokes Equations ◽  
Vertical Walls ◽  
Curved Walls

Fluid dynamics for a Newtonian fluid in the absence of body forces in a two-dimensional cavity with top and bottom curved walls was studied numerically. The vertical walls are fixed and the curved walls are in motion. The Navier-Stokes equations were solved using the finite element method combined with the operator splitting scheme. We analyzed the behaviour of the velocity fields, the vorticity fields and the velocity profiles of the fluid inside the cavity. The analysis was carried out for two different Reynolds numbers of 50 and 500 with two ratios (R = 1, −1) of the top to the bottom curved lid speed. For these values of parameters the flow is characterized by vortex formation inside the cavity. The spatial symmetry on the flow patterns are also investigated. We found that when the velocities of the top and bottom walls have opposite direction only one cell is formed in the central part of the cavity; however when the velocities of the top and bottom walls have the same direction the vortex formation inside the cavity is more complex.

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