Conservative interpolation for the boundary integral solution of the Navier-Stokes equations

2000 ◽  
Vol 26 (6) ◽  
pp. 507-513 ◽  
Author(s):  
W. F. Florez ◽  
H. Power ◽  
F. Chejne
Keyword(s):  
Stokes Equations ◽  
Boundary Integral ◽  
Integral Solution ◽  
Navier Stokes ◽  
Navier Stokes Equations

Meshless velocity – vorticity local boundary integral equation (LBIE) method for two dimensional incompressible Navier-Stokes equations

2019 ◽  
Vol 29 (11) ◽  
pp. 4034-4073 ◽  
Author(s):  
E.J. Sellountos ◽  
Jorge Tiago ◽  
Adelia Sequeira
Keyword(s):  
Integral Equation ◽  
Boundary Integral Equation ◽  
Stokes Equations ◽  
Boundary Integral ◽  
Integral Representations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Content Type ◽  
Local Boundary ◽  
Local Boundary Integral Equation

Purpose This paper aims to describe the 2D meshless local boundary integral equation (LBIE) method for solving the Navier–Stokes equations. Design/methodology/approach The velocity–vorticity formulation is selected to eliminate the pressure gradient of the equations. The local integral representations of flow kinematics and transport kinetics are derived. The integral equations are discretized using the local RBF interpolation of velocities and vorticities, while the unknown fluxes are kept as independent variables. The resulting volume integrals are computed using the general radial transformation algorithm. Findings The efficiency and accuracy of the method are illustrated with several examples chosen from reference problems in computational fluid dynamics. Originality/value The meshless LBIE method is applied to the 2D Navier–Stokes equations. No derivatives of interpolation functions are used in the formulation, rendering the present method a robust numerical scheme for the solution of fluid flow problems.

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.

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