The subiteration method, which forms the basic iterative procedure for solving fluid-structure-interaction problems, is based on a partitioning of the fluid-structure system into a fluidic part and a structural part. In fluid-structure interaction, on short time scales the fluid appears as an added mass to the structural operator, and the stability and convergence properties of the subiteration process depend significantly on the ratio of this apparent added mass to the actual structural mass. In the present paper, we establish that the added-mass effects corresponding to compressible and incompressible flows are fundamentally different. For a model problem, we show that on increasingly small time intervals, the added mass of a compressible flow is proportional to the length of the time interval, whereas the added mass of an incompressible flow approaches a constant. We then consider the implications of this difference in proportionality for the stability and convergence properties of the subiteration process, and for the stability and accuracy of loosely coupled staggered time-integration methods.

1.
Farhat
,
C.
,
Geuzaine
,
P.
, and
Brown
,
G.
, 2003, “
Application of a Three-Field Nonlinear Fluidstructure Formulation to the Prediction of the Aeroelastic Parameters of an f-16 Fighter
,”
Comput. Fluids
0045-7930,
32
, pp.
3
29
.
2.
Farhat
,
C.
, 2004, “
CFD-Based Nonlinear Computational Aeroelasticity
,”
Encyclopedia of Computational Mechanics
, Vol.
3
: Fluids,
E.
Stein
,
R.
Borst
, and
T.
Hughes
, eds.,
Wiley
,
New York
, pp.
459
480
.
3.
Torii
,
R.
,
Oshima
,
M.
,
Kobayashi
,
T.
,
Takagi
,
K.
, and
Tezduyar
,
T.
, 2006, “
Computer Modeling of Cardiovascular Fluid-Structure Interaction With the Deforming-Spatial-Domain/Stabilized-Space-Time Formulation
,”
Comput. Methods Appl. Mech. Eng.
0045-7825,
195
, pp.
1885
1895
.
4.
Tezduyar
,
T.
,
Sathe
,
S.
,
Cragin
,
T.
,
Nanna
,
B.
,
Conklin
,
B.
,
Pausewag
,
J.
, and
Schwaab
,
M.
, 2007, “
Modeling of Fluid-Structure Interactions With the Space-Time Finite Elements: Arterial Fluid Mechanics
,”
Int. J. Numer. Methods Fluids
0271-2091,
54
, pp.
901
922
.
5.
Michler
,
C.
,
van Brummelen
,
H.
, and
de Borst
,
R.
, 2006, “
Error-Amplification Analysis of Subiteration-Preconditioned GMRES for Fluid-Structure Interaction
,”
Comput. Methods Appl. Mech. Eng.
0045-7825,
195
, pp.
2124
2148
.
6.
Heil
,
M.
, 2004, “
An Efficient Solver for the Fully-Coupled Solution of Large-Displacement Fluid-Structure Interaction Problems
,”
Comput. Methods Appl. Mech. Eng.
0045-7825,
193
, pp.
1
23
.
7.
van Brummelen
,
H.
,
van der Zee
,
K.
, and
de Borst
,
R.
, 2008, “
Space/Time Multigrid for a Fluid-Structure-Interaction Problem
,”
Appl. Numer. Math.
,
58
(
12
), pp.
1951
1971
. 0045-7825
8.
Piperno
,
S.
, and
Farhat
,
C.
, 2001, “
Partitioned Procedures for the Transient Solution of Coupled Aeroelastic Problems—Part II: Energy Transfer Analysis and Three-Dimensional Applications
,”
Comput. Methods Appl. Mech. Eng.
0045-7825,
190
, pp.
3147
3170
.
9.
Felippa
,
C.
,
Park
,
K.
, and
Farhat
,
C.
, 2001, “
Partitioned Analysis of Coupled Mechanical Systems
,”
Comput. Methods Appl. Mech. Eng.
0045-7825,
190
, pp.
3247
3270
.
10.
Causin
,
P.
,
Gerbeau
,
J.
, and
Nobile
,
F.
, 2005, “
Added-Mass Effect in the Design of Partitioned Algorithms for Fluid-Structure Problems
,”
Comput. Methods Appl. Mech. Eng.
0045-7825,
194
, pp.
4506
4527
.
11.
LeTallec
,
P.
, and
Mouro
,
J.
, 2001, “
Fluid Structure Interaction With Large Structural Displacements
,”
Comput. Methods Appl. Mech. Eng.
0045-7825,
190
, pp.
3039
3067
.
12.
Förster
,
C.
,
Wall
,
W.
, and
Ramm
,
E.
, 2007, “
Artificial Added Mass Instabilities in Sequential Staggered Coupling of Nonlinear Structures and Incompressible Viscous Flows
,”
Comput. Methods Appl. Mech. Eng.
0045-7825,
196
, pp.
1278
1293
.
13.
Tezduyar
,
T.
,
Sathe
,
S.
,
Keedy
,
R.
, and
Stein
,
K.
, 2006, “
Space-Time Finite Element Techniques for Computation of Fluid-Structure Interactions
,”
Comput. Methods Appl. Mech. Eng.
,
195
, pp.
2002
2027
. 0045-7825
14.
Tezduyar
,
T.
, 2006, “
Interface-Tracking and Interface-Capturing Techniques for Finite Element Computation of Moving Boundaries and Interfaces
,”
Comput. Methods Appl. Mech. Eng.
,
195
, pp.
2983
3000
. 0045-7825
15.
Zauderer
,
E.
, 1989,
Partial Differential Equations of Applied Mathematics
,
(Pure and Applied Mathematics)
,
2nd ed.
,
Wiley
,
Chichester, West Sussex, UK
.
16.
Haberman
,
R.
, 1998,
Applied Partial Differential Equations
,
3rd ed.
,
Pearson Prentice-Hall
,
Upper Saddle River, NJ
.
17.
van Brummelen
,
H.
, and
de Borst
,
R.
, 2005, “
On the Nonnormality of Subiteration for a Fluid-Structure Interaction Problem
,”
SIAM J. Sci. Comput. (USA)
1064-8275,
27
, pp.
599
621
.
This content is only available via PDF.
You do not currently have access to this content.