Abstract
The main focus of the present article is the development of a general solution framework for coupled and/or interaction multi-physics problems based upon re-using existing codes into software products. In particular, we discuss how to build this software tool for the case of fluid–structure interaction problem, from finite element code FEAP for structural and finite volume code OpenFOAM for fluid mechanics. This is achieved by using the Component Template Library (CTL) to provide the coupling between the existing codes into a single software product. The present CTL code-coupling procedure accepts not only different discretization schemes, but different languages, with the solid component written in Fortran and fluid component written in C++ . Moreover, the resulting CTL-based code also accepts the nested parallelization. The proposed coupling strategy is detailed for explicit and implicit fixed-point iteration solver presented in the Part I of this paper, referred to Direct Force-Motion Transfer/Block- Gauss-Seidel. However, the proposed code-coupling framework can easily accommodate other solution schemes. The selected application examples are chosen to confirm the capability of the code-coupling strategy to provide a quick development of advanced computational tools for demanding practical problems, such as 3D fluid models with free-surface flows interacting with structures.
Similar content being viewed by others
References
Adams MF, Bayraktar HH, Keaveny TM, Panayiotis P (2004) Ultrascalable implicit finite element analyses in solid mechanics with over a half billion degrees of freedom. In: SC2004 High performance computing, networking and storage conference, Pittsburg, PA
Austruy C, Kassiotis C, Colliat J-B, Ibrahimbegovic A, Matthies HG, Dias F (2008) A multiscale and multiphysic approach to quantify waves damping by structures. In: Ibrahimbegovic A, Zlatar M (eds) NATO–ARW 983112 damage assessments and reconstruction after natural disasters and previous military activities, Sarajevo, Bosnia-Herzegovina, October 2008
Barcelos M, Bavestrello H, Maute K (2006) A Schur– Newton–Krylov solver for steady-state aeroelastic analysis and design sensitivity analysis. Comput Methods Appl Mech Eng 195: 2050–2069
Barton IE (1998) Comparison of SIMPLE- and PISO-type algorithms for transient flows. Int J Numer Methods Fluid 26(4): 459–483
Bathe K-J, Zhang H (2009) A mesh adaptivity procedure for CFD and fluid-structure interactions. Comput Struct 87(11–12): 604–617
Bazilevs Y, Calo VM, Hughes TJR, Zhang Y (2008) Isogeometric fluid-stucture interaction: theory, algorithms and computations. Comput Mech 43: 3–37
Bazilevs Y, Calo VM, Zhang Y, Hughes TJR (2006) Isogeometric fluid-structure interaction analysis with applications to arterial blood flow. Computat Mech 38: 310–322
Bazilevs Y, Gohean JR, Hughes TJR, Moser RD, Zhang Y (2009) Patient-specific isogeometric fluid-structure interaction analysis of thoraci aortic blood flow due to implation of the jarvik 2000 left ventricular assist device. Comput Methods Appl Mech Eng 198: 3534–3550
Bazilevs Y, Hsu M-C, Benson D, Sankaran S, Marsden A (2009) Computational fluid-structure interaction: methods and application to a total cavopulmonary connection. Comput Mech 45: 77–89
Bazilevs Y, Hsu M-C, Zhang Y, Kvamsdal T, Hentschel S, Isaksen J (2010) Computational fluid-structure interaction: Methods and application to cerebral aneurysms. Biomech Model Mechanobiol 9: 481–498
Beckert A, Wendland H (2001) Multivariate interpolation for fluid-structure-interaction problems using radial basis functions. Aerosp Sci Technol 5(2): 125–134
Behzadi A, Issa RI, Rusche H (2004) Modelling of dispersed bubble and droplet flow at high phase fractions. Chem Eng Sci 59(4): 759–770
Belytschko T (1983) An overview of semidiscretization and time integration procedures. In: Belytschko T, Hughes TJR (eds) Computational methods for transient analysis. North-Holland, Amsterdam, pp 1–65. Journal of Applied Mechanics
Belytschko T, Kam Liu W, Moran B (2000) Nonlinear finite elements for continua and structures. Wiley, New York
Causin P, Gerbeau J-F, Nobile F (2005) Added-mass effect in the design of partitioned algorithms for fluid-structure problems. Comput Methods Appl Mech Eng 194(42–44): 4506–4527
Chorin AJ (1967) A numerical method for solving incompressible viscous flow problems. J Comput Phys 2(1): 12–26
Chung J, Hulbert GM (1994) A family of single-step houbolt time integration algorithms for structural dynamics. Comput Methods Appl Mech Eng 118(1–2): 1–11
Dalrymple RA, Rogers BD (2006) Numerical modeling of water waves with the SPH method. Coast Eng 53(2–3): 141–147
de Boer A, van Zuijlen AH, Bijl H (2007) Review of coupling methods for non-matching meshes. Comput Methods Appl Mech Eng 196(8): 1515–1525
Degroote J, Bathe K-J, Vierendeels J (2009) Performance of a new partitioned procedure versus a monolithic procedure in fluid-structure interaction. Comput Struct 87(11–12): 793–801
Demirdžić I, Perić M (1988) Space conservation law in finite volume calculations of fluid flow. Int J Numer Methods Fluid 8(9): 1037–1050
Deparis S, Discacciati M, Fourestey G, Quarteroni A (2006) Fluid-structure algorithms based on Steklov-Poincaré operators. Comput Methods Appl Mech Eng 195(41–43): 5797–5812
Dettmer WG, Perić D (2007) A fully implicit computational strategy for strongly coupled fluid-solid interaction. Arch Comput Methods Eng 14: 205–247
Farhat C, Geuzaine P, Grandmont C (2001) The discrete geometric conservation law and the nonlinear stability of ale schemes for the solution of flow problems on moving grids. J Comput Phys 174(2): 669–694
Farhat C, Lesoinne M (2000) Two efficient staggered algorithms for the serial and parallel solution of three-dimensional nonlinear transient aeroelastic problems. Comput Methods Appl Mech Eng 182: 499–515
Farhat C, Lesoinne M, Maman N (1995) Mixed explicit/implicit time integration of coupled aeroelastic problems: three-field formulation, geometric conservation and distributed solution. Int J Numer Methods Eng 21(10): 807–835
Felippa CA, Park KC (2004) Synthesis tools for structural dynamics and partitioned analysis of coupled systems. In: Ibrahimbegović A, Brank B (eds) NATO advanced research workshop, pp 50–111
Felippa CA, Park KC, de Runtz JA (1977) Stabilization of staggered solution procedures for fluid-structure interaction analysis. In: Computational methods for fluid-structure interaction problems, pp 95–124
Fernández MÁ, Moubachir M (2005) A Newton method using exact Jacobians for solving fluid–structure coupling. Comput Struct 83(2–3): 127–142
Ferziger JH, Perić M (2002) Computational methods for fluid dynamics, 3rd edn. Springler-Verlag, Berlin
Förster C, Wall WA, Ramm E (2006) On the geometric conservation law in transient ow calculations on deforming domains. Int J Numer Methods Fluid 50: 1369–1379
Förster C, Wall WA, Ramm E (2007) Artificial added mass instabilities in sequential staggered coupling of nonlinear structures and incompressible viscous flows. Comput Methods Appl Mech Eng 196: 1278–1291
Fosdick LD, Jessup ER, Schauble CJC, Domik G (1996) An introduction to high-performance scientific computing. The MIT Press, Cambridge
Franca LP, Hughes TJR, Stenberg R (1993) Stabilized finite element methods. In: Incompressible computational fluid dynamics, pp 87–107
Ghidaglia J-M, Kumbaro A, Le Coq G (2001) On the numerical solution to two-fluid models via a cell centered finite volume method. Eur J Mech B Fluids 20(6): 841–867
Ghidaglia J-M, Pascal F (2005) The normal flux method at the boundary for multidimensional finite volume approximations in CFD. Eur J Mech B Fluids 24(1): 1–17
Glowinski R (2003) Numerical methods for fluids (Part III). In: Ciarlet PG, Lions JL (eds) Handbook of numerical analysis, vol 9. Elsevier, North-Holland
Hautefeuille M (2009) Numerical modeling strategy for heterogeneous materials: a FE multi-scale and component-based approach. PhD thesis, Université Technologique de Compiègne, Technische Universität Braunschweig and École Normale Supérieure de Cachan, France and Germany
Heil M (2004) An efficient solver for the fully coupled solution of large-displacement fluid–structure interaction problems. Comput Methods Appl Mech Eng 193(1–2): 1–23
Hilber HM, Hughes TJR, Taylor RL (1977) Improved numerical dissipation for time integration algorithms in structural dynamics. Earthq Eng Struct Dyn 5(3): 283–292
Hübner B, Walhorn E, Dinkler D (2004) A monolithic approach to fluid-structure interaction using space-time finite elements. Comput Methods Appl Mech Eng 193: 2087–2104
Hughes TJR, Pister KS, Taylor RL (1979) Implicit-explicit finite elements in nonlinear transient analysis. Comput Methods Appl Mech Eng 17: 159–182
Hughes TJR, Franca LP, Balestra M (1986) A new finite element formulation for computational fluid dynamics: V. Circumventing the Babuška–Brezzi condition: a stable Petrov–Galerkin formulation of the Stokes problem accommodating equal-order interpolations. Comput Methods Appl Mech Eng 59: 85–99
Ibrahimbegovic A (2009) Nonlinear solid mechanics: theoretical formulations and finite element solution methods. Springer, New York
Ibrahimbegovic A, Gresovnik I, Markovic D, Melnyk S, Rodic T (2005) Shape optimization of two-phase inelastic material with microstructure. Eng Comput 22(5–6): 605–645
Ibrahimbegovic A, Knopf-Lenoir C, Kucerova A, Villon P (2004) Optimal design and optimal control of elastic structures undergoing finite rotations. Int J Numer Methods Eng 61(14): 2428–2460
Ibrahimbegovic A, Markovič D (2003) Strong coupling methods in multi-phase and multi-scale modeling of inelastic behavior of heterogeneous structures. Comput Methods Appl Mech Eng 192: 3089–3107
Issa RI (1986) Solution of the implicitly discretised fluid flow equations by operator-splitting. J Comput Phys 62(1): 40–65
Issa RI, Ahmadi-Befrui B, Beshay KR, Gosman AD (1991) Solution of the implicitly discretised reacting flow equations by operator-splitting. J Comput Phys 93: 388–410
Jasak H (2009) OpenFOAM: open source CFD in research and industry. Int J Naval Archit Ocean Eng 1(2): 89–94
Joosten MM, Dettmer WG, Perić D (2009) Analysis of the block Gauss-Seidel solution procedure for a strongly coupled model problem with reference to fluid-structure interaction. Int J Numer Methods Eng 78(7): 757–778
Jürgens D (2009) Survey on software engineering for scientific applications. Informatikbericht, Institute for Scientific Computing, Braunschweig, Germany
Karypis G, Kumar V (1998) METIS, a software package for partitioning unstructured graphs, partitioning meshes, and computing fill-reducing orderings of sparse matrices. University of Minnesota, Department of Computer Science, Minneapolis, MN, USA. http://www.cs.umn.edu/~karypis
Kassiotis C, Colliat J-B, Ibrahimbegovic A, Matthies HG (2009) Multiscale in time and stability analysis of operator split solution procedure applied to thermomechanical problems. Eng Comput 1–2: 205–223
Kassiotis C, Ibrahimbegovic A, Matthies HG (2010) Partitioned solution to fluid-structure interaction problems in application to free-surface flows. Eur J Mech B Fluids (accepted)
Krosche M (2009) Ofoam’s manual. Informatikbericht, Institute for Scientific Computing, Braunschweig, Germany (in preparation)
Küttler U, Förster C, Wall WA (2006) A solution for the incompressibility dilemma in partitioned fluid-structure interaction with pure Dirichlet fluid domains. Comput Mech 38: 417–429
Küttler U, Wall WA (2008) Fixed-point fluid-structure interaction solvers with dynamic relaxation. Computat Mech 43(1): 61–72
Le Tallec P, Mouro J (2001) Fluid structure interaction with large structural displacements. Comput Methods Appl Mech Eng 190(24–25): 3039–3067
Legay A, Chessa J, Belytschko T (2006) An eulerian-lagrangian method for fluid-structure interaction based on level sets. Comput Methods Appl Mech Eng 195(17–18): 2070–2087
Leveque RJ (1996) High-resolution conservative algorithms for advection in incompressible flow. Soc Ind Appl Math J Numer Anal 33(2): 627–665
Markovič D, Niekamp R, Ibrahimbegovic A, Matthies HG, Taylor RL (2005) Multi-scale modeling of heterogeneous structures with inelastic constitutive behavior: mathematical and physical aspects. Int J Eng Comput 22: 664–683
Matthies HG, Niekamp R, Steindorf J (2006) Algorithms for strong coupling procedures. Comput Methods Appl Mech Eng 195: 2028–2049
Matthies HG, Steindorf J (2003) Partitioned strong coupling algorithms for fluid-structure interaction. Comput Struct 81: 805–812
Mehl M, Brenk M, Bungartz HJ, Daubner K, Muntean IL, Neckel T (2008) An Eulerian approach for partitioned fluid-structure simulations on Cartesian grids. Comput Mech 43(1): 115–124
Mittal S, Tezduyar TE (1995) Parallel finite element simulation of 3D incompressible flows—fluid-structure interactions. Int J Numer Methods Fluid 21: 933–953
Monaghan JJ (1992) Smoothed particle hydrodynamics. Annu Rev Astron Astrophys 30(1): 543–574
Niekamp R, Markovič D, Ibrahimbegovic A, Matthies HG, Taylor RL (2009) Multi-scale modelling of heterogeneous structures with inelastic constitutive behavior. Part II: software coupling implementation aspects. Eng Comput 26: 6–28
Patankar SV (1980) Numerical heat transfer and fluid flow. Hemisphere Publishing Corporation, Washington
Patankar SV, Spalding DB (1972) A calculation procedure for heat, mass and momentum transfer in three-dimensional parabolic flows. Int J Heat Mass Transf 15(10): 1787–1806
Perić D, Dettmer WG, Saksono PH (2006) Modelling fluid-induced structural vibrations: reducing the structural risk for stormywinds. In: Ibrahimbegovic A (ed) NATO advanced research workshop, ARW 981641, Opatija, Croatia, pp 239–268
Piperno S, 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 190: 3147–3170
Rogers S, Kwak D, Kiris C (1991) Steady and unsteady solutions of the incompressible Navier-Stokes equations. Am Inst Aeronaut Astronaut J 29(4): 603–610
Ross MR, Sprague MA, Felippa CA, Park KC (2009) Treatment of acoustic fluid-structure interaction by localized Lagrange multipliers and comparison to alternative interface-coupling methods. Comput Methods Appl Mech Eng 198(9–12): 986–1005
Takizawa K, Moorman C, Wright S, Christopher J, Tezduyar T (2010) Wall shear stress calculations in spacetime finite element computation of arterial fluidstructure interactions. Comput Mech 46(1): 31–41
Tezduyar T, Takizawa K, Moorman C, Wright S, Christopher J (2010) Multiscale sequentially-coupled arterial FSI technique. Comput Mech 46(1): 17–29
Tezduyar TE, Mittal S, Ray SE, Shih R (1992) Incompressible flow computations with stabilized bilinear and linear equal-order interpolation velocity-pressure elements. Comput Methods Appl Mech Eng 95: 221–242
Tezduyar TE, Sathe S (2007) Modelling of fluid-structure interactions with the space-time finite elements: solution techniques. Int J Numer Methods Fluids 54(6–8): 855–900
Tezduyar TE, Sathe S, Keedy R, Stein K (2006) Space–time finite element techniques for computation of fluid–structure interactions. Comput Methods Appl Mech Eng 195(17–18): 2002–2027
Tezduyar TE, Sathe S, Pausewang J, Schwaab M, Christopher J, Crabtree J (2008) Interface projection techniques for fluid–structure interaction modeling with moving-mesh methods. Comput Mech 43(1): 39–49
Turek S, Hron J (2006) Proposal for numerical benchmarking of fluid-structure interaction between an elastic object and laminar incompressible flow. Lect Notes Comput Sci Eng 53: 371
Ubbink O, Issa RI (1999) A method for capturing sharp fluid interfaces on arbitrary meshes. J Comput Phys 153(1): 26–50
Van Doormaal JP, Raithby GD (1984) Enhancements of the SIMPLE method for predicting incompressible fluid flows. Numer Heat Transf A Appl 7(2): 147–163
von Scheven M (2009) Effiziente Algorithmen für die Fluid-Struktur-Wechselwirkung. PhD thesis, Institut für Baustatik und Baudynamik, Universität Stuttgart, Germany
Wall WA, Mok DP, Ramm E (1999) Partitioned analysis approach of the transient coupled response of viscous fluids and flexible structures. In: Solids, structures and coupled problems in engineering. Proceedings of the European conference on computational mechanics
Wang H, Belytschko T (2009) Fluid-structure interaction by the discontinuous-Galerkin method for large deformations. Int J Numer Methods Eng 77(1): 30–49
Zienkiewicz OC, Taylor RL (2001) The finite element method. The basis, vol 1, 5th edn. Butterworth Heinemann, Oxford
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Kassiotis, C., Ibrahimbegovic, A., Niekamp, R. et al. Nonlinear fluid–structure interaction problem. Part II: space discretization, implementation aspects, nested parallelization and application examples. Comput Mech 47, 335–357 (2011). https://doi.org/10.1007/s00466-010-0544-7
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00466-010-0544-7