Numerical stabilities of loosely coupled methods for robust modeling of lightweight and flexible structures in incompressible and viscous flows 
期刊名称Acta Mechanica Sinica
作者Deniz Tolga Akcabay; Jian Xiao; Yin Lu Young
摘要The growing interest to examine the hydroelastic dynamics and stabilities of lightweight and flexible materials requires robust and accurate fluid-structure interaction (FSI) models. Classically, partitioned fluid and structure solvers are easier to implement compared to monolithic methods; however, partitioned FSI models are vulnerable to numerical ("virtual added mass") instabilities for cases when the solid to fluid density ratio is low and if the flow is incompressible. As a partitioned method, the loosely hybrid coupled (LHC) method, which was introduced and validated in Young et al. (Acta Mech. Sin. 28:1030-1041, 2012), has been successfully used to efficiently and stably model lightweight and flexible structures. The LHC method achieves its numerical stability by, in addition to the viscous fluid forces, embedding potential flow approximations of the fluid induced forces to transform the partitioned FSI model into a semi-implicit scheme. The objective of this work is to derive and validate the numerical stability boundary of the LHC. The results show that the stability boundary of the LHC is much wider than traditional loosely coupled methods for a variety of numerical integration schemes. The results also show that inclusion of an estimate of the fluid inertial forces is the most critical to ensure the numerical stability when solving for fluid-structure interaction problems involving cases with a solid to fluid-added mass ratio less than one.
关键词Numericalstability; Fluid-structureinteraction; Loosely hybrid coupling method; Incompressible flow; Partitioned methods; Lightweight structures
参考文献1. Akcabay, D. T., Young, Y. L.:Hydroelastic response and energy harvesting potential of flexible piezoelectric beams in viscous flow. Phys. Fluids 24, 054106 (2012)  
2. Bazilevs, Y., Hsu, M. -C., Kiendl, J., et al.:3D simulation of wind turbine rotors at full scale. Part b:fluid-structure interaction modeling with composite blades. Int. J. Numer. Method. Fluids 65, 236-253 (2011)
3. Dumont, Vierendeels J., Verdonck, P. R.:A partitioned strongly coupled fluid-structure interaction method to model heart valve dynamics. J. Comput. Appl. Math. 215, 602-609 (2008)  
4. Young, Y. L.:Fluid-structure interaction analysis of flexible composite marine propellers. J. Fluids Struct. 24, 799-818 (2008)  
5. Lian, Y., Shyy W.:Three-dimensional fluid-structure interactions of a membrane wing for micro air vehicle applications. In:44th AIAA, ASME, ASCE, AHS Structures, Structural Dynamics, and Materials Conference, Norfolk, April 7-10 (2003). doi:10. 2514/6. 2003-1726
6. Leroyer, A., Visonneau, M.:Numerical methods for RANSE simulations of a self-propelled fish-like body. J. Fluids Struct. 20, 975-991 (2005)  
7. Motley, M. R., Young, Y. L.:Scaling of the transient hydroelastic response and failure mechanisms of self-adaptive composite marine propellers. Int. J. Rotat. Mach. 2012, 632856 (2012)
8. Akcabay, D. T., Young, Y. L.:Scaling the dynamic response and energy harvesting potential of piezoelectric beams. Appl. Phys. Lett. 101, 264104 (2012). doi:10. 1063/1. 4773210  
9. Young, Y. L.:Dynamic hydroelastic scaling of self-adaptive composite marine rotors. Compos. Struct. 92, 97-106 (2010)  
10. Heil, M.:An efficient solver for the fully coupled solution of large-displacement fluid-structure interaction problems. Comput. Method. Appl. Mech. Eng. 193, 1-23 (2004)  
11. Hübner, B., Walhorn, E., Dinkler, D.:A monolithic approach to fluid-structure interaction using space-time finite elements. Comput. Method. Appl. Mech. Eng. 193, 2087-2104 (2004)  
12. Ishihara, D., Yoshimura, S.:A monolithic approach for interaction of incompressible viscous fluid and an elastic body based on fluid pressure poisson equation. Int. J. Numer. Method. Eng. 64, 167-203 (2005)  
13. Bathe, K. -J., Zhang, H.:Finite element developments for general fluid flows with structural interactions. Int. J. Numer. Method. Eng. 60, 213-232 (2004)  
14. Longatte, E., Verreman, V., Souli, M.:Time marching for simulation of fluid-structure interaction problems. J. Fluids Struct. 25, 95-111 (2009)  
15. Fernández, M. A., Gerbeau, J. -F., Grandmont, C.:A projection semi-implicit scheme for the coupling of an elastic structure with an incompressible fluid. Int. J. Numer. Method. Eng. 69, 794-821 (2007)  
16. Förster, C., Wall, W. A., Ramm, E.:Artificial added mass instabilities in sequential staggered coupling of nonlinear structures and incompressible viscous flows. Comput. Method. Appl. Mech. Eng. 196, 1278-1293 (2007)  
17. Küttler, U., Wall, W. A.:Fixed-point fluid-structure interaction solvers with dynamic relaxation. Comput. Mech. 43, 61-72 (2008)  
18. Badia, S., Nobile, F., Vergara, C.:Fluid-structure partitioned procedures based on robin transmission conditions. J. Comput. Phys. 227, 7027-7051 (2008)  
19. Young, Y. L., Chae, E. J., Akcabay, D. T.:Hybrid algorithm for modeling of fluid-structure interaction in incompressible viscous flows. Acta Mech. Sin. 28, 1030-1041 (2012)  
20. Degroote, J., Bruggeman, P., Haelterman, R., et al.:Stability of a coupling technique for partitioned solvers in FSI applications. Comput. Struct. 86, 2224-2234 (2008)  
21. van Brummelen, E. H.:Added mass effects of compressible and incompressible flows in fluid-structure interaction. J. Appl. Mech. 76, 021206 (2009)  
22. Vierendeels, J., Dumont, K., Dick, E., et al.:Analysis and stabilization of fluid-structure interaction algorithm for rigid-body motion. AIAA J. 43, 2549-2557 (2005)  
23. Causin, P., Gerbeau, J. F., Nobile, F.:Added-mass effect in the designofpartitionedalgorithmsforfluid-structureproblems. Comput. Method. Appl. Mech. Eng. 194, 4506-4527 (2005)  
24. Belanger, F., Païdoussis, M. P., de Langre, E.:Time-marching analysis of fluid-coupled systems with large added mass. AIAA J. 33, 752-757 (1995)  
25. Idelsohn, S. R., Del Pin, F., Rossi, R., et al.:Fluid-structure interaction problems with strong added-mass effect. Int. J. Numer. Method. Eng. 80, 1261-1294 (2009)  
26. Douglas Jr., J., Dupont, T.:Alternating-Direction Galerkin Methods on Rectangles, Numerical Solution of Partial Differential Equations, b (SYNSPADE 1970). Academic Press, New York (1971)
27. Smereka, P.:Semi-implicit level set methods for curvature and surface diffusion motion. J. Sci. Comput. 19, 439-456 (2003)  
28. Xu, J. -J., Zhao, H. -K.:An Eulerian formulation for solving partial differential equations along a moving interface. J. Sci. Comput. 19, 573-594 (2003)  
29. Ceniceros, H. D., Hou, T. Y.:An efficient dynamically adaptive mesh for potentially singular solutions. J. Comput. Phys. 172, 609-639 (2001)  
30. Baek, H., Karniadakis, G. E.:A convergence study of a new partitioned fluid-structure interaction algorithm based on fictitious mass and damping. J. Comput. Phys. 231, 629-652 (2012)  
31. Connell, B. S. H., Yue, D. K. P.:Flapping dynamics of a flag in a uniform stream. J. Fluid Mech. 581, 33-67 (2007)  
32. Chae, E. J., Akcabay, D. T., Young, Y. L.:Dynamic response and stability of a flapping foil in a dense viscous fluid. Phys. Fluids 25, 104106 (2013)  
33. Akcabay, D. T., Ducoin, A., Chae, E. J., et al.:Transient hydroelastic response of a flexible hydrofoil in subcavitating and cavitating flows. In:29th Symposium on Naval Hydrodynamics. Gothenburg, Sweden (2012)
34. Akcabay, D. T., Young, Y. L.:Influence of cavitation on the hydroelastic stability of hydrofoils. J. Fluids Struct. 49, 170-185 (2014)  
35. Akcabay, D. T., Chae, E. J., Young, Y. L., et al.:Cavity induced vibration of flexible hydrofoils. J. Fluids Struct. 49, 463-484 (2014)  
36. Akcabay, D. T., Young, Y. L.:Parametric excitations and lock-in of flexible hydrofoils in two-phase flows. J. Fluids Struct. 57, 344-356 (2015)  
37. Kring, D. C.:Time domain ship motions by a three-dimensional Rankine panel method,[Ph. D. Thesis], Massachusetts Institute of Technology, USA (1994)
38. Theodorsen, T.:General theory of aerodynamic instability and the mechanism of flutter. National Advisory Committee for Aeronautics Report, No. 496 (1935)
39. Fung, Y. C.:An Introduction to the Theory of Aeroelasticity. Dover Publications, New York (1993)
40. Münch, C., Ausoni, P., Braun, O., et al.:Fluid-structure coupling for an oscillating hydrofoil. J. Fluids Struct. 26, 1018-1033 (2010)  
41. Roth, S., Calmon, M., Farhat, M., et al.:Hydrodynamic damping identification from an impulse response of a vibrating blade. In:Proceedings of the 3rd IAHR International Meeting of the Workgroup on Cavitation and Dynamic Problems in Hydraulic Machinery and Systems, Brno, Czech Republic (2009)
42. ANSYS:ANSYS CFX-Solver Modeling guide. Release 14. 0. ANSYS Inc., Canonsburg (2011)
43. Brennen, C. E.:A review of added mass and fluid inertial forces, Report No. CR 82. 010, Department of the Navy, Naval Civil Engineering Laboratory. Port Hueneme, CA, USA (1982)
44. Young, Y. L., Motley, M. R., Barber, R., et al.:Adaptive composite marine propulsors and turbines:progress and challenges. Appl. Mech. Rev. 68, 062001 (2016)
作者地址Department of Naval Architecture and Marine Engineering, University of Michigan, 2600 Draper Dr., Ann Arbor, MI 48109-2145, USA

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