In the computation of a three–dimensional steady creeping flow around a rigid body, the total body force and torque are well predicted using a boundary integral equation (BIE) with a single concentrated pair Stokeslet- Rotlet located at an interior point of the body. However, the distribution of surface tractions are seldom considered. Then, a completed indirect velocity BIE of Fredholm type and second-kind is employed for the computation of the pointwise tractions, and it is numerically solved by using either collocation or Galerkin weighting procedures over flat triangles. In the Galerkin case, a full numerical quadrature is proposed in order to handle the weak singularity of the tensor kernels, which is an extension for fluid engineering of a general framework (Taylor, 2003, “Accurate and Efficient Numerical Integration of Weakly Singulars Integrals in Galerkin EFIE Solutions,” IEEE Trans. on Antennas and Propag., 51(7), pp. 1630–1637). Several numerical simulations of steady creeping flow around closed bodies are presented, where results compare well with semianalytical and finite-element solutions, showing the ability of the method for obtaining the viscous drag and capturing the singular behavior of the surface tractions close to edges and corners. Also, deliberately intricate geometries are considered.

References

References
1.
Beer
,
G.
, and
Watson
,
J. O.
,
1992
, “Introduction to Finite and Boundary Element Method for Engineers,” Wiley, UK.
2.
Sauter
,
S. A.
, and
Schwab
,
C.
,
2011
,
Boundary Element Methods
,
Springer-Verlag
,
Berlin-Heidelberg
.
3.
Stenroos
,
M.
, and
Haueisen
,
J.
,
2008
, “
Boundary Element Computations in the Forward and Inverse Problems of Electrocardiography: Comparison of Collocation and Galerkin Weightings
,”
IEEE Trans. Biomed. Eng.
,
55
(
9
), pp.
2124
2133
.10.1109/TBME.2008.923913
4.
Fata
,
S. N.
,
2009
, “
Explicit Expressions for 3D Boundary Integrals in Potential Theory
,”
Int. J. for Num. Meth. Eng.
,
78
, pp.
32
47
.10.1002/nme.2472
5.
Scuderi
,
L.
,
2008
, “
On the Computation of Nearly Singular Integrals in 3D BEM Collocation
,”
Int. J. Numer. Methods Eng.
,
74
, pp.
1733
1770
.10.1002/nme.2229
6.
D'Elía
,
J.
,
Storti
,
M. A.
, and
Idelsohn
,
S. R.
,
2000
, “
A Closed Form for Low Order Panel Methods
,”
Adv. Eng. Software
,
31
(
5
), pp.
335
341
.10.1016/S0965-9978(99)00060-5
7.
D'Elía
,
J.
,
Storti
,
M. A.
, and
Idelsohn
,
S. R.
,
2000
, “
A Panel-Fourier Method for Free Surface Methods
,”
Trans ASME J. Fluids Eng.
,
122
(
2
), pp.
309
317
.10.1115/1.483259
8.
D'Elía
,
J.
,
Battaglia
,
L.
, and
Storti
,
M.
,
2011
, “
A Semi-Analytical Computation of the Kelvin Kernel for Potential Flows With a Free Surface
,”
Comp. Appl. Math
,
30
(
2
), pp.
267
287
.10.1590/S1807-03022011000200002
9.
D'Elía
,
J.
,
Storti
,
M. A.
, and
Idelsohn
,
S. R.
,
2000
, “
Iterative Solution of Panel Discretizations for Potential Flows. The Modal/Multipolar Preconditioning
,”
Int. J. Numer. Methods
,
32
(
1
), pp.
1
22
.
10.
Alia
,
A. M. S.
, and
Erchiqui
,
F.
,
2006
, “
Variational Boundary Element Acoustic Modeling Over Mixed Quadrilateral–Triangular Element Meshes
,”
Comm. Numer. Methods Eng.
,
22
(
7
), pp.
767
780
.10.1002/cnm.848
11.
Bonnet
,
M.
,
Maier
,
G.
, and
Polizzotto
,
C.
,
1998
, “
Symmetric Galerkin Boundary Element Methods
,”
ASME Appl. Mech. Rev.
,
51
(
11
), pp.
669
704
.10.1115/1.3098983
12.
Sutradhar
,
A.
,
Paulino
,
G. H.
, and
Gray
,
L. J.
,
2008
,
Symmetric Galerkin Boundary Element Method
,
Springer
,
New York
.
13.
Salvadori
,
A.
,
2010
, “
Analytical Integrations in 3D BEM for Elliptic Problems: Evaluation and Implementation
,”
Int. J. Numer. Methods Eng.
,
84
(
5
), pp.
505
542
.10.1002/nme.2906
14.
Power
,
H.
, and
Wrobel
,
L. C.
,
1995
,
Boundary Integral Methods in Fluid Mechanics
,
Computational Mechanics Publications
,
Southampton, UK
.
15.
D'Elía
,
J.
,
Battaglia
,
L.
,
Storti
,
M.
, and
Cardona
,
A.
,
2009
, “
Galerkin Boundary Integral Equations Applied to Three Dimensional Stokes Flows
,”
Mecánica Computacional
,
C.
Bauza
,
P.
Lotito
,
L.
Parente
, and
M.
Vénere
, eds., pp.
1453
1462
, Vol.
XXVIII
.
16.
Ladyzhenskaya
,
O. A.
,
1969
,
The Mathematical Theory of Viscous Incompressible Flow
,
2nd ed.
,
Gordon and Breach
,
New York
.
17.
Dargush
,
G. F.
, and
Grigoriev
,
M. M.
,
2005
, “
Fast and Accurate Solutions of Steady Stokes Flows Using Multilevel Boundary Element Methods
,”
ASME J. Fluids Eng.
,
127
(
4
), pp.
640
646
.10.1115/1.1949648
18.
Lepchev
,
D.
, and
Weihs
,
D.
,
2010
, “
Low Reynolds Number Flow in Spiral Microchannels
,”
ASME J. Fluids Eng.
,
132,
(
7
), p.
071202
.10.1115/1.4001860
19.
Shipman
,
T. N.
,
Prasad
,
A. K.
,
Davidson
,
S. L.
, and
Cohee
,
D. R.
,
2007
, “
Particle Image Velocimetry Evaluation of a Novel Oscillatory-Flow Flexible Chamber Mixer
,”
ASME J. Fluids Eng.
,
129
(
2
), pp.
179
187
.10.1115/1.2409347
20.
Méndez
,
C.
,
Paquay
,
S.
,
Klapka
,
I.
, and
Raskin
,
J. P.
,
2008
, “
Effect of Geometrical Nonlinearity on MEMS Thermoelastic Damping
,”
Nonlinear Anal. R. World Appl.
,
10
(
3
), pp.
1579
1588
.10.1016/j.nonrwa.2008.02.002
21.
Berli
,
C.
, and
Cardona
,
A.
,
2009
, “
On the Calculation of Viscous Damping of Microbeam Resonators in Air
,”
J. Sound Vib.
,
327
(
1–2
), pp.
249
253
.10.1016/j.jsv.2009.06.003
22.
Galvis
,
E.
,
Yarusevych
,
S.
, and
Culham
,
J. R.
,
2012
, “
Incompressible Laminar Developing Flow in Microchannels
,”
ASME J. Fluid Eng.
,
134
(
1
), p.
014503
.10.1115/1.4005736
23.
Ingber
,
M. S.
, and
Mammoli
,
A. A.
,
1999
, “
A Comparison of Integral Formulations for the Analysis of Low Reynolds Number Flows
,”
Eng. Anal. Bound. Elem.
,
23
, pp.
307
315
.10.1016/S0955-7997(98)00090-3
24.
Power
,
H.
, and
Miranda
,
G.
,
1987
, “
Second Kind Integral Equation Formulation of Stokes Flows Past a Particle of Arbitrary Shape
,”
SIAM J. Appl. Math.
,
47
(
4
), pp.
689
698
.10.1137/0147047
25.
Kim
,
S.
, and
Karrila
,
S. J.
,
1991
,
Microhydrodynamics: Principles and Selected Applications
,
Butterworth
,
Washington, DC
.
26.
Ingber
,
M. S.
, and
Mondy
,
L. A.
,
1993
, “
Direct Second Kind Boundary Integral Formulation for Stokes Flow Problems
,”
Comput. Mech.
,
11
, pp.
11
27
.10.1007/BF00370070
27.
Fang
,
Z.
,
Mammoli
,
A. A.
, and
Ingber
,
M. S.
,
2001
, “
Analyzing Irreversibilities in Stokes Flows Containing Suspensed Particles Using the Traction Boundary Integral Equation Method
,”
Eng. Anal. Bound. Elem.
,
25
, pp.
249
257
.10.1016/S0955-7997(01)00024-8
28.
Keaveny
,
E. E.
, and
Shelley
,
M. J.
,
2011
, “
Applying a Second-Kind Boundary Integral Equation for Surface Tractions in Stokes Flow
,”
J. Comp. Phys.
,
230
, pp.
2141
2159
.10.1016/j.jcp.2010.12.010
29.
Hebeker
,
F. K.
,
1986
, “
Efficient Boundary Element Methods for Three-Dimensional Exterior Viscous Flow
,”
Numer. Methods PDE
,
2
(
4
), pp.
273
297
.10.1002/num.1690020404
30.
Gonzalez
,
O.
,
2009
, “
On Stable, Complete, and Singularity-Free Boundary Integral Formulations of Exterior Stokes Flow
,”
SIAM J. Appl. Math.
,
69
, pp.
933
958
.10.1137/070698154
31.
Taylor
,
D. J.
,
2003
, “
Accurate and Efficient Numerical Integration of Weakly Singulars Integrals in Galerkin EFIE Solutions
,”
IEEE Trans. Antennas Propag.
,
51
(
7
), pp.
1630
1637
.10.1109/TAP.2003.813623
32.
Mustakis
,
I.
, and
Kim
,
S.
,
1998
, “
Microhydrodynamics of Sharp Corners and Edges: Traction Singularities
,”
AIChE J.
,
44,
(
7
), pp.
1469
1483
.10.1002/aic.690440702
33.
Pozrikidis
,
C.
,
1997
,
Boundary Integral and Singularity Methods for Linearized Viscous Flow
,
Cambridge University
,
Cambridge, UK
.
34.
Amarakoon
,
A. M. D.
,
Hussey
,
R. G.
,
Good
,
B. J.
, and
Grimsal
,
E. G.
,
1982
, “
Drag Measurements for Axisymmetric Motion of a Torus at Low Reynolds Number
,”
Phys. Fluids
,
25
(
9
), pp.
1495
1501
.10.1063/1.863935
35.
Sarraf
,
S.
,
López
,
E.
,
Ríos Rodríguez
,
G.
, and
D'Elía
,
J.
,
2014
, “
Validation of a Galerkin Technique on a Boundary Integral Equation for Creeping Flow Around a Torus
,”
Comput. Appl. Math.
,
33
(
1
), pp.
63
80
.10.1007/s40314-013-0043-5
36.
Storti
,
M. A.
,
Nigro
,
N. M.
,
Paz
,
R. R.
, and
Dalcin
,
L. D.
,
2008
, “
Dynamic Boundary Conditions in Computational Fluid Dynamics
,”
Comp. Methods Appl. Mech. Eng.
,
197
(
13–16
), pp.
1219
1232
.10.1016/j.cma.2007.10.014
37.
Battaglia
,
L.
,
D'Elía
,
J.
,
Storti
,
M. A.
, and
Nigro
,
N. M.
,
2006
, “
Numerical Simulation of Transient Free Surface Flows
,”
ASME J. Appl. Mech.
,
73
(
6
), pp.
1017
1025
.10.1115/1.2198246
38.
Storti
,
M. A.
, and
D'Elía
,
J.
,
2004
, “
Added Mass of an Oscillating Hemisphere at Very-Low and Very-High Frequencies
,”
ASME J. Fluids Eng.
,
126
(
6
), pp.
1048
1053
.10.1115/1.1839932
39.
Brooks
,
A. N.
, and
Hughes
,
T. J. R.
,
1982
, “
Streamline Upwind/Petrov–Galerkin Formulations for Convection Dominated Flows With Particular Emphasis on the Incompressible Navier–Stokes Equations
,”
Comp. Methods Appl. Mech. Eng.
,
32
, pp.
199
259
.10.1016/0045-7825(82)90071-8
40.
Tezduyar
,
T. E.
,
Mittal
,
S.
,
Ray
,
S.
, and
Shih
,
R.
,
1992
, “
Incompressible Flow Computations With Stabilized Bilinear and Linear Equal Order Interpolation Velocity-Pressure Elements
,”
Comp. Methods Appl. Eng.
,
95
, pp.
221
242
.10.1016/0045-7825(92)90141-6
41.
Schöberl
,
J.
,
1997
, “
NETGEN - An Advancing Front 2D/3D-Mesh Generator Based on Abstract Rules
,”
Comp. and Vis. in Sci.
,
1
(1), p.
41
52
.
42.
Edelsbrunner
,
H.
,
2001
, “
180 Wrapped Tubes
,”
J. Univ. Comp. Sci.
,
7
(5), pp.
379
399
.
43.
D'Elía
,
J.
,
Battaglia
,
L.
,
Cardona
,
A.
, and
Storti
,
M.
,
2011
, “
Full Numerical Quadrature of Weakly Singular Double Surface Integrals in Galerkin Boundary Element Methods
,”
Int. J. Numer. Methods Biomed. Eng.
,
27
(
2
), pp.
314
334
.10.1002/cnm.1309
44.
Polimeridis
,
A. G.
, and
Mosig
,
J. R.
,
2010
, “
Complete Semi-Analytical Treatment of Weakly Singular Integrals on Planar Triangles Via the Direct Evaluation Method
,”
Int. J. Numer. Methods Eng.
,
83
(
12
), pp.
1625
1650
.10.1002/nme.2877
You do not currently have access to this content.