Hostname: page-component-76fb5796d-9pm4c Total loading time: 0 Render date: 2024-04-26T12:38:38.537Z Has data issue: false hasContentIssue false
  • English
  • Français

AC-CBS-Based Partitioned Semi-Implicit Coupling Algorithm for Fluid-Structure Interaction Using Stabilized Second-Order Pressure Scheme

Part of: Basic methods in fluid mechanics Coupling of solid mechanics with other effects Partial differential equations, initial value and time-dependent initial-boundary value problems Equations of mathematical physics and other areas of application

Published online by Cambridge University Press:  27 March 2017

Tao He ,
Kai Zhang  and
Tong Wang
Tao He*
Affiliation:
Department of Civil Engineering, Shanghai Normal University, Shanghai 201418, China School of Engineering, University of Birmingham, Birmingham B15 2TT, UK
Kai Zhang*
Affiliation:
School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, China Department of Civil Engineering, Graduate School of Urban Innovation, Yokohama National University, Yokohama 2408501, Japan
Tong Wang*
Affiliation:
Department of Civil Engineering, Shanghai Normal University, Shanghai 201418, China
*
*Corresponding author. Email addresses:txh317@bham.ac.uk (T. He), kai-zhang-kf@ynu.jp (K. Zhang), tongwang@shnu.edu.cn (T. Wang)
*Corresponding author. Email addresses:txh317@bham.ac.uk (T. He), kai-zhang-kf@ynu.jp (K. Zhang), tongwang@shnu.edu.cn (T. Wang)
*Corresponding author. Email addresses:txh317@bham.ac.uk (T. He), kai-zhang-kf@ynu.jp (K. Zhang), tongwang@shnu.edu.cn (T. Wang)
Get access

Abstract

We analyze in this paper the pressure splitting scheme of a partitioned semi-implicit coupling algorithm for fluid-structure interaction (FSI) simulation. The semi-implicit coupling algorithm is developed on the ground of the artificial compressibility characteristic-based split (AC-CBS) scheme that serves not only for the fluid subsystem but also for the global FSI system. As the dual-time stepping procedure recommended for quasi-incompressible flows is incorporated into the implicit coupling stage, the fluctuating pressure may be unusually susceptible to the AC coefficient. Moreover, it is not trivial to devise an optimal AC formulation for pressure estimation. Instead, we consider a stabilized second-order pressure splitting scheme in the AC-CBS-based partitioned semi-implicit coupling algorithm. Computer simulation of a benchmark FSI experiment demonstrates that good agreement is exposed between the available and present data.

Keywords

Fluid-structure interactionsemi-implicit couplingCBSartificial compressibilitysecond order

MSC classification

Secondary: 35Q30: Navier-Stokes equations 65M22: Solution of discretized equations 65M60: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods 74F10: Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) 76M10: Finite element methods
Type
Research Article
Information
Communications in Computational Physics , Volume 21 , Issue 5 , May 2017 , pp. 1449 - 1474
Copyright
Copyright © Global-Science Press 2017 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Liu, J, Jaiman, RK, Gurugubelli, PS. A stable second-order scheme for fluid–structure interaction with strong added-mass effects. Journal of Computational Physics 2014; 270:687–710.CrossRefGoogle Scholar
[2] Hu, Z, Tang, W, Xue, H, Zhang, X. A SIMPLE-based monolithic implicit method for strong-coupled fluid–structure interaction problems with free surfaces. Computer Methods in Applied Mechanics and Engineering 2016; 299:90–115.CrossRefGoogle Scholar
[3] Kang, W, Zhang, JZ, Feng, PH. Aerodynamic analysis of a localized flexible airfoil at low Reynolds numbers. Communications in Computational Physics 2012; 11(4):1300–1310.CrossRefGoogle Scholar
[4] He, T. On a partitioned strong coupling algorithm for modeling fluid–structure interaction. International Journal of Applied Mechanics 2015; 7(2):1550021.CrossRefGoogle Scholar
[5] Hou, G, Wang, J, Layton, A. Numerical methods for fluid-structure interaction—a review. Communications in Computational Physics 2012; 12(2):337–377.CrossRefGoogle Scholar
[6] He, T, Zhang, K. An overview of the combined interface boundary condition method for fluidstructure interaction. Archives of Computational Methods in Engineering 2016; doi: 10.1007/s11831-016-9193-0, in press.CrossRefGoogle Scholar
[7] Fernández, MA, Gerbeau, JF, Grandmont, C. A projection semi-implicit scheme for the coupling of an elastic structure with an incompressible fluid. International Journal for Numerical Methods in Engineering 2007; 69(4):794–821.CrossRefGoogle Scholar
[8] Causin, P, Gerbeau, JF, Nobile, F. Added-mass effect in the design of partitioned algorithms for fluid–structure problems. Computer Methods in Applied Mechanics and Engineering 2005; 194(42):4506–4527.CrossRefGoogle Scholar
[9] Förster, C, Wall, WA, Ramm, E. Artificial added mass instabilities in sequential staggered coupling of nonlinear structures and incompressible viscous flows. Computer Methods in Applied Mechanics and Engineering 2007; 196(7):1278–1293.CrossRefGoogle Scholar
[10] van Brummelen, EH. Added mass effects of compressible and incompressible flows in fluid-structure interaction. Journal of Applied Mechanics–ASME 2009; 76(2):021206.CrossRefGoogle Scholar
[11] Chorin, AJ. Numerical solution of the Navier-Stokes equations. Mathematics of Computation 1968; 22(104):745–762.CrossRefGoogle Scholar
[12] Témam, R. Une méthode d’approximation de la solution des équations de Navier-Stokes. Bulletin de la Société Mathématique de France 1968; 96:115–152.CrossRefGoogle Scholar
[13] Quaini, A, Quarteroni, A. A semi-implicit approach for fluid-structure interaction based on an algebraic fractional step method. Mathematical Models and Methods in Applied Sciences 2007; 17(06):957–983.CrossRefGoogle Scholar
[14] Badia, S, Quaini, A, Quarteroni, A. Splitting methods based on algebraic factorization for fluid–structure interaction. SIAM Journal on Scientific Computing 2008; 30(4):1778–1805.CrossRefGoogle Scholar
[15] Astorino, M, Chouly, F, Fernández, MA. Robin based semi-implicit coupling in fluid-structure interaction: Stability analysis and numerics. SIAM Journal on Scientific Computing 2009; 31(6):4041–4065.CrossRefGoogle Scholar
[16] Astorino, M, Grandmont, C. Convergence analysis of a projection semi-implicit coupling scheme for fluid–structure interaction problems. Numerische Mathematik 2010; 116(4):721–767.CrossRefGoogle Scholar
[17] Fernández, MA. Coupling schemes for incompressible fluid-structure interaction: implicit, semi-implicit and explicit. SeMA Journal 2011; 55(1):59–108.CrossRefGoogle Scholar
[18] Bertoglio, C, Moireau, P, Gerbeau, JF. Sequential parameter estimation for fluid–structure problems: Application to hemodynamics. International Journal for Numerical Methods in Biomedical Engineering 2012; 28(4):434–455.CrossRefGoogle ScholarPubMed
[19] He, T, Zhou, D, Han, Z, Tu, J, Ma, J. Partitioned subiterative coupling schemes for aeroelasticity using combined interface boundary condition method. International Journal of Computational Fluid Dynamics 2014; 28(6-10):272–300.CrossRefGoogle Scholar
[20] He, T. Partitioned coupling strategies for fluid–structure interaction with large displacement: Explicit, implicit and semi-implicit schemes. Wind & Structures 2015; 20(3):423–448.CrossRefGoogle Scholar
[21] He, T. Semi-implicit coupling of CS-FEM and FEM for the interaction between a geometrically nonlinear solid and an incompressible fluid. International Journal of Computational Methods 2015; 12(5):1550025.CrossRefGoogle Scholar
[22] He, T, Zhang, K. Combined interface boundary condition method for fluid–structure interaction: Some improvements and extensions. Ocean Engineering 2015; 109:243–255.CrossRefGoogle Scholar
[23] He, T. A CBS-based partitioned semi-implicit coupling algorithm for fluid–structure interaction using MCIBC method. Computer Methods in Applied Mechanics and Engineering 2016; 298:252–278.CrossRefGoogle Scholar
[24] Sy, S, Murea, CM. A stable time advancing scheme for solving fluid–structure interaction problem at small structural displacements. Computer Methods in Applied Mechanics and Engineering 2008; 198(2):210–222.CrossRefGoogle Scholar
[25] Murea, CM, Sy, S. A fast method for solving fluid–structure interaction problems numerically. International Journal for Numerical Methods in Fluids 2009; 60(10):1149–1172.CrossRefGoogle Scholar
[26] Breuer, M, De Nayer, G, Münsch, M, Gallinger, T, Wüchner, R. Fluid–structure interaction using a partitioned semi-implicit predictor–corrector coupling scheme for the application of large-eddy simulation. Journal of Fluids and Structures 2012; 29:107–130.CrossRefGoogle Scholar
[27] Jan, YJ, Sheu, TWH. Finite element analysis of vortex shedding oscillations from cylinders in the straight channel. Computational Mechanics 2004; 33(2):81–94.CrossRefGoogle Scholar
[28] Chorin, AJ. A numerical method for solving incompressible viscous flow problems. Journal of Computational Physics 1967; 2(1):12–26.CrossRefGoogle Scholar
[29] Turkel, E. Preconditioned methods for solving the incompressible and low speed compressible equations. Journal of Computational Physics 1987; 72(2):277–298.CrossRefGoogle Scholar
[30] Zienkiewicz, OC, Nithiarasu, P, Codina, R, Vazquez, M, Ortiz, P. The characteristic-based-split procedure: An efficient and accurate algorithm for fluid problems. International Journal for Numerical Methods in Fluids 1999; 31(1):359–392.3.0.CO;2-7>CrossRefGoogle Scholar
[31] Nithiarasu, P, Codina, R, Zienkiewicz, OC. The Characteristic-Based Split (CBS) scheme–a unified approach to fluid dynamics. International Journal for Numerical Methods in Engineering 2006; 66(10):1514–1546.CrossRefGoogle Scholar
[32] Douglas, J Jr, Russell, TF. Numerical methods for convection-dominated diffusion problems based on combining the method of characteristics with finite element or finite difference procedures. SIAM Journal on Numerical Analysis 1982; 19(5):871–885.CrossRefGoogle Scholar
[33] Löhner, R, Morgan, K, Zienkiewicz, OC. The solution of non-linear hyperbolic equation systems by the finite element method. International Journal for Numerical Methods in Fluids 1984; 4(11):1043–1063.CrossRefGoogle Scholar
[34] Codina, R, Blasco, J. Stabilized finite element method for the transient Navier–Stokes equations based on a pressure gradient projection. Computer Methods in Applied Mechanics and Engineering 2000; 182(3):277–300.CrossRefGoogle Scholar
[35] Nithiarasu, P, Zienkiewicz, OC. Analysis of an explicit andmatrix free fractional step method for incompressible flows. Computer Methods in Applied Mechanics and Engineering 2006; 195(41):5537–5551.CrossRefGoogle Scholar
[36] Codina, R, Blasco, J. A finite element formulation for the Stokes problem allowing equal velocity-pressure interpolation. Computer Methods in Applied Mechanics and Engineering 1997; 143(3):373–391.CrossRefGoogle Scholar
[37] Codina, R. Pressure stability in fractional step finite element methods for incompressible flows. Journal of Computational Physics 2001; 170(1):112–140.CrossRefGoogle Scholar
[38] Bao, Y, Zhou, D, Huang, C. Numerical simulation of flow over three circular cylinders in equilateral arrangements at low Reynolds number by a second-order characteristic-based split finite element method. Computers & Fluids 2010; 39(5):882–899.CrossRefGoogle Scholar
[39] Codina, R, Vázquez, M, Zienkiewicz, OC. A general algorithm for compressible and incompressible flows. Part III: The semi-implicit form. International Journal for Numerical Methods in Fluids 1998; 27(1-4):13–32.3.0.CO;2-8>CrossRefGoogle Scholar
[40] Tang, HS, Sotiropoulos F. Fractional step artificial compressibility schemes for the unsteady incompressible Navier-Stokes equations. Computers & Fluids 2007; 36(5):974–986.CrossRefGoogle Scholar
[41] Nithiarasu, P. An efficient artificial compressibility (AC) scheme based on the characteristic based split (CBS) method for incompressible flows. International Journal for Numerical Methods in Engineering 2003; 56(13):1815–1845.CrossRefGoogle Scholar
[42] Nithiarasu, P. An arbitrary Lagrangian Eulerian (ALE) formulation for free surface flows using the characteristic-based split (CBS) scheme. International Journal for Numerical Methods in Fluids 2005; 48(12):1415–1428.CrossRefGoogle Scholar
[43] Wood, C, Gil, AJ, Hassan, O, Bonet, J. Partitioned block-Gauss–Seidel coupling for dynamic fluid–structure interaction. Computers & Structures 2010; 88(23):1367–1382.CrossRefGoogle Scholar
[44] Könözsy, L, Drikakis, D. A unified fractional-step, artificial compressibility and pressure-projection formulation for solving the incompressible Navier-Stokes equations. Communications in Computational Physics 2014; 16(5):1135–1180.CrossRefGoogle Scholar
[45] Normura, T, Hughes, TJR. An arbitrary Lagrangian-Eulerian finite element method for interaction of fluid and a rigid body. Computer Methods in Applied Mechanics and Engineering 1992; 95(1):115–138.Google Scholar
[46] Newmark, NM. A method of computation for structural dynamics. Journal of Engineering Mechanics–ASCE 1959; 85(3):67–94.Google Scholar
[47] Hilber, HM, Hughes, TJR, Taylor, RL. Improved numerical dissipation for time integration algorithms in structural dynamics. Earthquake Engineering & Structural Dynamics 1977; 5(3):283–292.CrossRefGoogle Scholar
[48] Chung, J, Hulbert, GM. A time integration algorithm for structural dynamics with improved numerical dissipation: The Generalized-α method. Journal of Applied Mechanics–ASME 1993; 60(2):371–375.CrossRefGoogle Scholar
[49] Bathe, KJ, Baig, MMI. On a composite implicit time integration procedure for nonlinear dynamics. Computers & Structures 2005; 83(31):2513–2524.CrossRefGoogle Scholar
[50] De Rosis, A, Falcucci, G, Ubertini, S, Ubertini, F. A coupled lattice Boltzmann-finite element approach for two-dimensional fluid-structure interaction. Computers & Fluids 2013; 86:558–568.CrossRefGoogle Scholar
[51] De Rosis, A, Falcucci, G, Ubertini, S, Ubertini, F, Succi, S. Lattice Boltzmann analysis of fluid-structure interaction with moving boundaries. Communications in Computational Physics 2013; 13(3):823–834.CrossRefGoogle Scholar
[52] De Rosis, A, Ubertini, S, Ubertini, F. A partitioned approach for two-dimensional fluid–structure interaction problems by a coupled lattice Boltzmann-finite element method with immersed boundary. Journal of Fluids and Structures 2014; 45:202–215.CrossRefGoogle Scholar
[53] Dettmer, W, Perić, D. A computational framework for fluid–rigid body interaction: Finite element formulation and applications. Computer Methods in Applied Mechanics and Engineering 2006; 195(13):1633–1666.CrossRefGoogle Scholar
[54] Lefrançois, E. A simple mesh deformation technique for fluid–structure interaction based on a submesh approach. International Journal for Numerical Methods in Engineering 2008; 75(9):1085–1101.CrossRefGoogle Scholar
[55] Markou, GA, Mouroutis, ZS, Charmpis, DC, Papadrakakis, M. The ortho-semi-torsional (OST) spring analogy method for 3D mesh moving boundary problems. Computer Methods in Applied Mechanics and Engineering 2007; 196(4):747–765.CrossRefGoogle Scholar
[56] Zeng, D, Ethier, CR. A semi-torsional spring analogy model for updating unstructured meshes in 3D moving domains. Finite Elements in Analysis and Design 2005; 41(11):1118–1139.CrossRefGoogle Scholar
[57] Souli, M, Ouahsine, A, Lewin, L. ALE formulation for fluid–structure interaction problems. Computer Methods in Applied Mechanics and Engineering 2000; 190(5):659–675.CrossRefGoogle Scholar
[58] Liu, X, Qin, N, Xia, H. Fast dynamic grid deformation based on Delaunay graph mapping. Journal of Computational Physics 2006; 211(2):405–423.CrossRefGoogle Scholar
[59] Piperno, S. Explicit/implicit fluid/structure staggered procedures with a structural predictor and fluid subcycling for 2D inviscid aeroelastic simulations. International Journal for Numerical Methods in Fluids 1997; 25(10):1207–1226.3.0.CO;2-R>CrossRefGoogle Scholar
[60] Mok, DP, Wall, WA. Partitioned analysis schemes for the transient interaction of incompressible flows and nonlinear flexible structures. In Trends in Computational Structural Mechanics, Wall, WA, Bletzinger, KU, Schweizerhof, K (eds.), CIMNE: Barcelona, Spain, 2001; 689–698.Google Scholar
[61] Küttler, U, Wall, WA. Fixed-point fluid-structure interaction solvers with dynamic relaxation. Computational Mechanics 2008; 43(1):61–72.CrossRefGoogle Scholar
[62] Badia, S, Codina, R. On some fluid–structure iterative algorithms using pressure segregation methods. Application to aeroelasticity. International Journal for Numerical Methods in Engineering 2007; 72(1):46–71.CrossRefGoogle Scholar
[63] Küttler, U, Förster, C, Wall, WA. A solution for the incompressibility dilemma in partitioned fluid–structure interaction with pure Dirichlet fluid domains. Computational Mechanics 2006; 38(4-5):417–429.CrossRefGoogle Scholar
[64] Irons, BM, Tuck, RC. A version of the Aitken accelerator for computer iteration. International Journal for Numerical Methods in Engineering 1969; 1(3):275–277.CrossRefGoogle Scholar
[65] Baek, H, Karniadakis, GE. A convergence study of a new partitioned fluid–structure interaction algorithm based on fictitious mass and damping. Journal of Computational Physics 2012; 231(2):629–652.CrossRefGoogle Scholar
[66] Anagnostopoulos, P, Bearman, P. Response characteristics of a vortex-excited cylinder at low Reynolds numbers. Journal of Fluids and Structures 1992; 6(1):39–50.CrossRefGoogle Scholar
[67] Roshko, A. On the development of turbulent wakes from vortex streets. Technical Report NACA TN 1191, National Advisory Committee for Aeronautics 1954.Google Scholar
[68] He, T, Zhou, D, Bao, Y. Combined interface boundary condition method for fluid–rigid body interaction. Computer Methods in Applied Mechanics and Engineering 2012; 223:81–102.CrossRefGoogle Scholar
[69] He, T. A partitioned implicit coupling strategy for incompressible flow past an oscillating cylinder. International Journal of Computational Methods 2015; 12(2):1550012.CrossRefGoogle Scholar
[70] Young, DL, Chang, JT, Eldho, TI. A coupled BEM and arbitrary Lagrangian–Eulerian FEM model for the solution of two-dimensional laminar flows in external flow fields. International Journal for Numerical Methods in Engineering 2001; 51(9):1053–1077.CrossRefGoogle Scholar
[71] Chern, MJ, Kuan, YH, Nugroho, G, Lu, GT, Horng, TL. Direct-forcing immersed boundary modeling of vortex-induced vibration of a circular cylinder. Journal of Wind Engineering and Industrial Aerodynamics 2014; 134:109–121.CrossRefGoogle Scholar
[72] Samaniego, C, Houzeaux, G, Samaniego, E, Vázquez, M. Parallel embedded boundary methods for fluid and rigid-body interaction. Computer Methods in Applied Mechanics and Engineering 2015; 290:387–419.CrossRefGoogle Scholar
[73] Wei, R, Sekine, A, Shimura, M. Numerical analysis of 2D vortex-induced oscillations of a circular cylinder. International journal for Numerical Methods in Fluids 1995; 21(10):993–1005.CrossRefGoogle Scholar
[74] Schulz, KW, Kallinderis, Y. Unsteady flow structure interaction for incompressible flows using deformable hybrid grids. Journal of Computational Physics 1998; 143(2):569–597.CrossRefGoogle Scholar
[75] Li, L, Sherwin, SJ, Bearman, PW. A moving frame of reference algorithm for fluid/structure interaction of rotating and translating bodies. International Journal for Numerical Methods in Fluids 2002; 38(2):187–206.CrossRefGoogle Scholar
[76] Abdullah, MM, Walsh, KK, Grady, S, Wesson, GD. Modeling flow around bluff bodies. Journal of Computing in Civil Engineering–ASCE 2005; 19(1):104–107.CrossRefGoogle Scholar
[77] Yang, J, Preidikman, S, Balaras, E. A strongly coupled, embedded-boundary method for fluid–structure interactions of elastically mounted rigid bodies. Journal of Fluids and Structures 2008; 24(2):167–182.CrossRefGoogle Scholar
[78] Yang, FL, Chen, CH, Young, DL. A novel mesh regeneration algorithm for 2D FEM simulations of flowswithmoving boundary. Journal of Computational Physics 2011; 230(9):3276–3301.CrossRefGoogle Scholar
[79] Takashi, N. ALE finite element computations of fluid-structure interaction problems. Computer Methods in Applied Mechanics and Engineering 1994; 112(1):291–308.CrossRefGoogle Scholar
[80] Bahmani, MH, Akbari, MH. Effects of mass and damping ratios on VIV of a circular cylinder. Ocean Engineering 2010; 37(5):511–519.CrossRefGoogle Scholar
[81] Nagaoka, S, Nakabayashi, Y, Yagawa, G, Kim, YJ. Accurate fluid-structure interaction computations using elements without mid-side nodes. Computational Mechanics 2011; 48(3):269–276.CrossRefGoogle Scholar
[82] Williamson, CHK, Roshko, A. Vortex formation in the wake of an oscillating cylinder. Journal of Fluids and Structures 1988; 2(4):355–381.CrossRefGoogle Scholar