ASYMPTOTIC ANALYSIS AND PARTIAL ASYMPTOTIC DECOMPOSITION OF DOMAIN FOR STOKES EQUATION IN TUBE STRUCTURE

1999 ◽  
Vol 09 (09) ◽  
pp. 1351-1378 ◽  
Author(s):  
F. BLANC ◽  
O. GIPOULOUX ◽  
G. PANASENKO ◽  
A. M. ZINE
Keyword(s):  
Asymptotic Expansion ◽  
Asymptotic Analysis ◽  
Boundary Layers ◽  
Stokes Problem ◽  
Navier Stokes ◽  
Thin Domain ◽  
Asymptotic Decomposition ◽  
Small Parts ◽  
Rod Structures ◽  
Tube Structure

The Stokes problem posed in tube structures (or finite rod structures (see Panasenko10)), i.e. in connected finite unions of the thin cylinders with the ratio of the diameter to the height of the order [Formula: see text], is considered. The asymptotic expansion of the solution is built and justified. Boundary layers are studied. Earlier the Navier–Stokes problem in one thin domain was considered by Nazarov.8 The method of asymptotic partial decomposition of the domain (MAPDD) (see Panasenko11) is applied and justified for the Stokes problem posed in a tube structures. This method reduces the initial Stokes problem to the Stokes problem in some small parts of the domain (where the boundary layers are "concentrated".)

ASYMPTOTIC METHODS FOR MICROPOLAR FLUIDS IN A TUBE STRUCTURE

2004 ◽  
Vol 14 (05) ◽  
pp. 735-758 ◽  
Author(s):  
D. DUPUY ◽  
G. P. PANASENKO ◽  
R. STAVRE
Keyword(s):  
Boundary Layer ◽  
Asymptotic Expansion ◽  
Small Parameter ◽  
Asymptotic Methods ◽  
Steady Motion ◽  
Asymptotic Decomposition ◽  
Micropolar Fluids ◽  
Layer Method ◽  
Boundary Layer Method ◽  
Tube Structure

The steady motion of a micropolar fluid through a wavy tube with the dimensions depending on a small parameter is studied. An asymptotic expansion is proposed and error estimates are proved by using a boundary layer method. We apply the method of partial asymptotic decomposition of domain and we prove that the solution of the partially decomposed problem represents a good approximation for the solution of the considered problem.

scholarly journals ON SINGULAR SOLUTIONS OF THE STATIONARY NAVIER-STOKES SYSTEM IN POWER CUSP DOMAINS

2021 ◽  
Vol 26 (4) ◽  
pp. 651-668
Author(s):  
Konstantinas Pileckas ◽  
Alicija Raciene
Keyword(s):  
Asymptotic Expansion ◽  
Stokes System ◽  
Boundary Value ◽  
Singular Solutions ◽  
Navier Stokes ◽  
Asymptotic Decomposition ◽  
Dirichlet Integral ◽  
Existence Of A Solution ◽  
Source Sink ◽  
Formal Asymptotic Expansion

The boundary value problem for the steady Navier–Stokes system is considered in a 2D bounded domain with the boundary having a power cusp singularity at the point O. The case of a boundary value with a nonzero flow rate is studied. In this case there is a source/sink in O and the solution necessarily has an infinite Dirichlet integral. The formal asymptotic expansion of the solution near the singular point is constructed and the existence of a solution having this asymptotic decomposition is proved.

scholarly journals Time periodic Navier–Stokes equations in a thin tube structure

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
R. Juodagalvytė ◽  
G. Panasenko ◽  
K. Pileckas
Keyword(s):  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Thin Tube ◽  
Time Periodic ◽  
Tube Structure

Essential Ingredients for the Computation of Steady and Unsteady Blade Boundary Layers

1991 ◽  
Vol 113 (4) ◽  
pp. 608-616 ◽  
Author(s):  
H. M. Jang ◽  
J. A. Ekaterinaris ◽  
M. F. Platzer ◽  
T. Cebeci
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Stokes Equations ◽  
Inviscid Flow ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Transitional Region ◽  
Low Reynolds Numbers ◽  
Flow Equations ◽  
Low Reynolds

Two methods are described for calculating pressure distributions and boundary layers on blades subjected to low Reynolds numbers and ramp-type motion. The first is based on an interactive scheme in which the inviscid flow is computed by a panel method and the boundary layer flow by an inverse method that makes use of the Hilbert integral to couple the solutions of the inviscid and viscous flow equations. The second method is based on the solution of the compressible Navier–Stokes equations with an embedded grid technique that permits accurate calculation of boundary layer flows. Studies for the Eppler-387 and NACA-0012 airfoils indicate that both methods can be used to calculate the behavior of unsteady blade boundary layers at low Reynolds numbers provided that the location of transition is computed with the en method and the transitional region is modeled properly.

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