A scalable and efficient monolithic approach based on the Balancing Domain Decomposition (BDD) method for acoustic fluid-structure interaction problems is developed. The BDD method is a well-known domain decomposition method for non-overlapping sub-domains, which consists of Neumann-Neumann (NN) preconditioning and coarse grid correction. In this study, we derive four types of BDD method, considering two options for NN preconditioning (NN-I and NN-C) and two options for coarse grid correction (CGC-FULL and CGC-DIAG). From the results of numerical experiments, the combination of NN-I and CGC-FULL turns out to be the most efficient scheme, showing fast convergence property irrespective of the number of sub-domains, DOFs of fluid and solid domains, and the added-mass effect of fluid. The combination of NN-I and CGC-DIAG is also expected to be an efficient scheme in some situations in a parallel environment.
References
1.
Ohayon
, R.
, 2001, “Reduced Symmetric Models for Modal Analysis of Internal Structural-Acoustic and Hydroelastic-Sloshing Systems
,” Comput. Meth. Appl. Mech. Eng.
, 190
, pp. 3009
–3019
.2.
Morland
, H. J. -P. J.-P.
, and Ohayon
, R.
, 1995, Fluid Structure Interaction - Applied Numerical Methods.
John Wiley & Sons
, New York.
3.
Mandel
, J.
, 2002, “An Iterative Substructuring Method for Coupled Fluid-Solid Acoustic Problems
,” J. Comput. Phys.
, 177
, pp. 95
–116
.4.
Ross
, M. R.
, Felippa
, C. A.
, Park
, K. C.
, and Sprague
, M. A.
, 2008, “Treatment of Acoustic Fluid-Structure Interaction by Localized Lagrange Multipliers: Formulation
,” Comput. Meth. Appl. Mech. Eng.
, 197
, pp. 3057
–3079
.5.
Park
, K. C.
, Felippa
, C. A.
, and Ohayon
, R.
, 2001, “Partitioned Formulation of Internal Fluid-Structure Interaction Problems by Localized Lagrange Multipliers
,” Comput. Meth. Appl. Mech. Eng.
, 190
(24–25
), pp. 2989
–3007
.6.
Takizawa
, K.
, Moorman
, C.
, Wright
, S.
, Spielman
, T.
, and Tezduyar
, T. E.
, 2011, “Fluid-Structure Interaction Modeling and Performance Analysis of the Orion Spacecraft Parachutes
,” Int. J. Numer. Methods Fluids
, 65
, pp. 271
–285
.7.
Takizawa
, K.
, Wright
, S.
, Moorman
, C.
, and Tezduyar
, T. E.
, 2011, “Fluid-Structure Interaction Modeling of Parachute Clusters
,” Int. J. Numer. Methods Fluids
, 65
, pp. 286
–307
.8.
Kalro
,V.
, and Tezduyar
, T. E.
, 2000, “A Parallel 3D Computational Method for Fluid-Structure Interactions in Parachute Systems
,” Comput. Meth. Appl. Mech. Eng.
, 190
, pp. 321
–332
.9.
Le Tallec
, P.
, and Mouro
, J.
, 2001, “Fluid Structure Interaction with Large Structural Displacements
,” Comput. Meth. Appl. Mech. Eng.
, 190
(24–25
), pp. 3039
–3067
.10.
Matthies
, H. G.
, Niekamp
, R.
, and Steindorf
, J.
, 2006, “Algorithms for Strong Coupling Procedures
,” Comput. Meth. Appl. Mech. Eng.
, 195
, pp. 2028
–2049
.11.
Michler
, C.
, van Brummelen
, E. H.
, and de Borst
, R.
, 2005, “An Interface Newton-Krylov Solver for Fluid-Structure Interaction
,” Int. J. Numer. Methods Fluids
, 47
(10–11
), pp. 1189
–1195
.12.
Heil
, M.
, 2004, “An Efficient Solver for the Fully-Coupled Solution of Large-Displacement Fluid-Structure Interaction Problems
,” Comput. Meth. Appl. Mech. Eng.
, 193
, pp. 1
–23
.13.
Ishihara
, D.
, and Yoshimura
, S.
, 2005, “A Monolithic Approach for Interaction of Incompressible Viscous Fluid and an Elastic Body Based on Fluid Pressure Poisson Equation
,” Int. J. Numer. Meth. Eng.
, 64
, pp. 167
–203
.14.
Liew
, K. M.
, Wang
, W. Q.
, Zhang
, L. X.
, and He
, X. Q.
, 2007, “A Computational Approach for Predicting the Hydroelasticity of Flexible Structures Based on the Pressure Poisson Equation
,” Int. J. Numer. Meth. Eng.
72
, pp. 1560
–1583
.15.
Washio
, T.
, Hisada
, T.
, Watanabe
, H.
, and Tezduyar
, T. E.
, 2005, “A Robust Preconditioner for Fluid-Structure Interaction Problems
,” Comput. Meth. Appl. Mech. Eng.
, 194
, pp. 4027
–4047
.16.
Badia
, S.
, Quaini
, A.
, and Quarteroni
, A.
, 2008, “Modular vs. Non-Modular Preconditioners for Fluid-Structure Systems With Large Added-Mass Effect
,” Comput. Meth. Appl. Mech. Eng.
, 197
, pp. 4216
–4232
.17.
Kuttler
, U.
, Gee
, M. W.
, Forster
, Ch.
, Comerford
, A.
, and Wall
, W. A.
, 2010, “Coupling Strategies for Biomedical Fluid-Structure Interaction Problems
,” Int. J. Numer. Meth. Biomed. Eng.
, 26
, pp. 305
–321
.18.
Tezduyar
, T. E.
, Sathe
, S.
, Keedy
, R.
, and Stein
, K.
, 2006, “Space-Time Finite Element Techniques for Computation of Fluid-Structure Interactions
,” Comput. Meth. Appl. Mech. Eng.
, 195
, pp. 2002
–2027
.19.
Tezduyar
, T. E.
, Sathe
, S.
, and Stein
, K.
, 2006, “Solution Techniques for the Fully Discretized Equations in Computation of Fluid-Structure Interactions With the Space-Time Formulations
,” Comput. Meth. Appl. Mech. Eng.
, 195
(41–43
), pp. 5743
–5753
.20.
Tezduyar
, T. E.
, and Sathe
, S.
, 2007, “Modeling of Fluid-Structure Interactions With the Space-Time Finite Elements: Solution Techniques
,” Int. J. Numer. Methods Fluids
, 54
, pp. 855
–900
.21.
Tezduyar
, T. E.
, Sathe
, S.
, Pausewang
, J.
, Schwaab
, M.
Christopher
, J.
, and Crabtree
, J.
, 2008, “Interface Projection Techniques for Fluid-Structure Interaction Modeling With Moving-Mesh Methods
,” Comput. Mech.
, 43
, pp. 39
–49
.22.
Tezduyar
, T. E.
, Sathe
, S.
, Schwaab
, M.
, Pausewang
, J.
, Christopher
, J.
, and Crabtree
, J.
, 2008, “Fluid-Structure Interaction Modeling of Ringsail Parachutes
,” Comput. Mech.
, 43
, pp. 133
–142
.23.
Manguoglu
, M.
, Takizawa
, K.
, Sameh
, A. H.
, and Tezduyar
, T. E.
, 2010, “Solution of Linear Systems in Arterial Fluid Mechanics Computations With Boundary Layer Mesh Refinement
,” Comput Mech.
, 46
, pp. 83
–89
.24.
Mandel
, J.
, 1993, “Balancing Domain Decomposition
,” Comm. Numer. Meth. Eng.
, 9
, pp. 233
–241
.25.
Shioya
, R.
, Ogino
, M.
, Kanayama
, H.
, and Tagami
, D.
, 2003, “Large Scale Finite Element Analysis with a Balancing Domain Decomposition Method
,” Key Eng. Mater.
, 243–244
, pp. 21
–26
.26.
Ogino
, M.
, Shioya
, R.
, and Kanayama
, H.
, 2008, “An Inexact Balancing Preconditioner for Large-Scale Structural Analysis
,” J. Comput. Sci. Tech.
, 2
(1
), pp. 150
–161
. 27.
Mukaddes
, A. M. M.
, Ogino
, M.
, Kanayama
, H.
, and Shioya
, R.
, 2006, “A Scalable Balancing Domain Decomposition Based Preconditioner for Large Scale Heat Transfer Problems
,” JSME Int. J. Series B
, 49
(2
), pp. 533
–540
.28.
Achdou
, Y.
, Le Tallec
, P.
, Nataf
, F.
, and Vidrascu
, M.
, 2000, “A Domain Decomposition Preconditioner for an Advection-Diffusion Problem
,” Comp. Meth. Appl. Mech. Eng.
, 184
, pp. 145
–170
.29.
Pavarino
, L. F.
, and Wildlund
, O. B.
, 2002, “Balancing Neumann-Neumann Methods for Incompressible Stokes Equations
,” Comm. Pure Appl. Math.
, 55
(3
), pp. 302
–335
.30.
Yao
, Q.
, Kanayama
, H.
, Notsu
, H.
, and Ogino
, M.
, 2010, “Balancing Domain Decomposition for Non-Stationary Incompressible Flow Problems Using a Characteristic-Curve Method
,” J. Comput. Sci. Tech.
, 4
(2
), pp. 121
–135
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