scholarly journals The boundary integral method for the steady rotating Navier–Stokes equations in exterior domain (I): the existence of solution

2009 ◽  
Vol 17 (1) ◽  
pp. 95-108 ◽  
Author(s):  
Rong An ◽  
Kaitai Li
Keyword(s):  
Integral Method ◽  
Exterior Domain ◽  
Stokes Equations ◽  
Existence Of Solution ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Domain I

Boundary integral method for the evolution of slender viscous fibres containing holes in the cross-section

2009 ◽  
Vol 621 ◽  
pp. 155-182 ◽  
Author(s):  
SRINATH S. CHAKRAVARTHY ◽  
WILSON K. S. CHIU
Keyword(s):  
Surface Tension ◽  
Cross Section ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Fibre Length ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Simply Connected

We consider the evolution of slender viscous fibres with cross-section containing holes with application to fabrication of microstructured optical fibres. The fibre evolution is driven by either prescribing velocity or a force at the ends of the fibre, and the free surfaces evolve under the influence of surface tension, internal pressurization, inertia and gravity. We use the fact that ratio of the typical fibre radius to the typical fibre length is small to perform an asymptotic analysis of the full three-dimensional Navier–Stokes equations similar to earlier work on non-axisymmetric (but simply connected) fibres. A numerical solution to the multiply connected steady-state drawing problem is formulated based on the solution the Sherman–Lauricella equation. The effects of different drawing and material parameters like surface tension, gravity, inertia and internal pressurization on the drawing are examined, and extension of the method to non-isothermal evolution is presented.

Solutions of the compressible Navier-Stokes equations using the integral method

AIAA Journal ◽  
1982 ◽  
Vol 20 (3) ◽  
pp. 356-362 ◽  
Author(s):  
M. M. EIRefaee ◽  
J. C. Wu ◽  
S. G. Lekoudis
Keyword(s):  
Integral Method ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations
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