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Multi-Level Acceleration of Parallel Coupled Partitioned Fluid-Structure Interaction with Manifold Mapping

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Book cover Recent Trends in Computational Engineering - CE2014

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 105))

Abstract

Strongly coupled fluid-structure interaction simulations often suffer from slow convergence, limited parallel scalability or difficulties in using black-box solvers. As partitioned simulations still play an important role in cases where new combinations of models, discretizations and codes have to be tested in an easy and fast way, we propose a combination of a parallel black-box coupling with a manifold mapping algorithm as an acceleration method. In this approach, we combine a computationally inexpensive low-fidelity FSI model with a high-fidelity FSI model to reduce the number of coupling iterations of the high fidelity FSI model. Information from previous time steps is taken into account with a secant update step similar to the Broyden update. The used black-box approach is applied for an incompressible laminar flow over a fixed cylinder with an attached flexible flap and a wave propagation in a three-dimensional elastic tube problem. A reduction of approximately 55 % in terms of high fidelity iterations is achieved compared to the Anderson mixing method if the fluid and the structure solvers are executed in parallel.

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Notes

  1. 1.

    http://www.extend-project.de/.

  2. 2.

    http://www.openfoam.org/.

References

  1. Anderson, D.G.: Iterative procedures for nonlinear integral equations. J. ACM 12(4), 547–560 (1965)

    Article  MATH  Google Scholar 

  2. Badia, S., Quaini, A., Quarteroni, A.: Modular vs. non-modular preconditioners for fluid-structure systems with large added-mass effect. Comput. Methods Appl. Mech. Eng. 197(49–50), 4216–4232 (2008)

    Google Scholar 

  3. Badia, S., Quaini, A., Quarteroni, A.: Splitting methods based on algebraic factorization for fluid-structure interaction. SIAM J. Sci. Comput. 30(4), 1778–1805 (2008). DOI 10.1137/070680497. URL http://www.rmee.upc.es/homes/badia/articles/art015.pdf

  4. Bandler, J.W., Biernacki, R.M., Chen, S.H., Grobelny, P.A., Hemmers, R.H.: Space mapping technique for electromagnetic optimization. IEEE Trans. Microwave Theory Tech. 42, 2536–2544 (1994)

    Article  Google Scholar 

  5. Bandler, J.W., Biernacki, R.M., Chen, S.H., Hemmers, R.H., Madsen, K.: Electromagnetic optimization exploiting aggressive space mapping. IEEE Trans. Microwave Theory Tech. 43(12), 2874–2882 (1995)

    Article  Google Scholar 

  6. Bandler, J.W., Cheng, Q.S., Dakroury, S.A., Mohamed, A.S., Bakr, M.H., Madsen, K., Søndergaard, J.: Space mapping: the state of the art. IEEE Trans. Microwave Theory Tech. 52(1), 337–361 (2004)

    Article  Google Scholar 

  7. Barker, A.T., Cai, X.C.: Scalable parallel methods for monolithic coupling in fluid–structure interaction with application to blood flow modeling. J. Comput. Phys. 229(3), 642–659 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  8. Bathe, K.J., Ledezma, G.A.: Benchmark problems for incompressible fluid flows with structural interactions. Comput. Struct. 85(11–14), 628–644 (2007)

    Article  Google Scholar 

  9. Bathe, K.J., Zhang, H.: A mesh adaptivity procedure for CFD and fluid-structure interactions. Comput. Struct. 87(11–12), 604–617 (2009)

    Article  Google Scholar 

  10. Blom, D.S., van Zuijlen, A.H., Bijl, H.: Acceleration of strongly coupled fluid-structure interaction with manifold mapping. In: Oñate, E., Oliver, X., Huerta, A. (eds.) Proceedings of the 11th World Congress on Computational Mechanics. 5th European Congress on Computational Mechanics. 6th European Congress on Computational Fluid Dynamics, pp. 4484–4495 (2014)

    Google Scholar 

  11. Blom, D.S., van Zuijlen, A.H., Bijl, H.: Multi-level acceleration with manifold mapping of strongly coupled fluid-structure interaction. Comput. Methods Appl. Mech. Eng. (2015)

    Google Scholar 

  12. Bogaers, A.E.J., Kok, S., Reddy, B.D., Franz, T.: Quasi-Newton methods for implicit black-box FSI coupling. Comput. Methods Appl. Mech. Eng. 279, 113–132 (2014)

    Article  MathSciNet  Google Scholar 

  13. Darwish, M., Sraj, I., Moukalled, F.: A coupled finite volume solver for the solution of incompressible flows on unstructured grids. J. Comput. Phys. 228(1), 180–201 (2009). DOI 10.1016/j.jcp.2008.08.027

    Article  MATH  MathSciNet  Google Scholar 

  14. de Boer, A., van Zuijlen, A.H., Bijl, H.: Radial Basis Functions for Interface Interpolation and Mesh Deformation. Lecture Notes in Computational Science and Engineering, vol. 71, Chap. 6, pp. 143–178. Springer, Berlin/Heidelberg (2010)

    Google Scholar 

  15. Degroote, J.: Partitioned simulation of fluid-structure interaction. Arch. Comput. Meth. Eng. 20(3), 185–238 (2013)

    Article  MathSciNet  Google Scholar 

  16. Degroote, J., Vierendeels, J.: Multi-solver algorithms for the partitioned simulation of fluid-structure interaction. Comput. Methods Appl. Mech. Eng. 200(25–28), 2195–2210 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  17. Degroote, J., Vierendeels, J.: Multi-level quasi-Newton coupling algorithms for the partitioned simulation of fluid-structure interaction. Comput. Methods Appl. Mech. Eng. 225–228, 14–27 (2012)

    Article  MathSciNet  Google Scholar 

  18. Degroote, J., Bruggeman, P., Haelterman, R., Vierendeels, J.: Stability of a coupling technique for partitioned solvers in FSI applications. Comput. Struct. 86, 2224–2234 (2008)

    Article  Google Scholar 

  19. Degroote, J., Bathe, K.J., Vierendeels, J.: Performance of a new partitioned procedure versus a monolithic procedure in fluid-structure interaction. Comput. Struct. 87(11–12), 793–801 (2009)

    Article  Google Scholar 

  20. Delinchant, B., Lahaye, D., Wurtz, F., Coulomb, J.L.: Manifold mapping optimization with or without true gradients. Math. Comput. Simul. 90, 256–265 (2013)

    Article  MathSciNet  Google Scholar 

  21. Echeverría, D., Hemker, P.W.: Space mapping and defect correction. Comput. Methods Appl. Math. 5(2), 107–136 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  22. Echeverría, D., Hemker, P.W.: Manifold mapping: a two-level optimization technique. Comput. Vis. Sci. 11(4–6), 193–206 (2008). DOI 10.1007/s00791-008-0096-y. URL http://dx.doi.org/10.1007/s00791-008-0096-y

  23. Echeverría, D., Lahaye, D., Encica, L., Lomonova, E.A., Hemker, P.W., Vandenput, A.J.A.: Manifold-mapping optimization applied to linear actuator design. IEEE Trans. Magn. 42(4), 1183–1186 (2006)

    Article  Google Scholar 

  24. Fang, H.R., Saad, Y.: Two classes of multisecant methods for nonlinear acceleration. Numer. Linear Algebra Appl. 16(3), 197–221 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  25. Farhat, C., Lesoinne, M.: Two efficient staggered algorithms for the serial and parallel solution of three-dimensional nonlinear transient aeroelastic problems. Comput. Methods Appl. Mech. Eng. 182(3–4), 499–515 (2000)

    Article  MATH  Google Scholar 

  26. Felippa, C., Park, K., Farhat, C.: Partitioned analysis of coupled mechanical systems. Comput. Methods Appl. Mech. Eng. 190(24–25), 3247–3270 (2001)

    Article  MATH  Google Scholar 

  27. Fernández, M.Á., Moubachir, M.: A Newton method using exact jacobians for solving fluid-structure coupling. Comput. Struct. 83(2–3), 127–142 (2005)

    Article  Google Scholar 

  28. Ganine, V., Hills, N.J., Lapworth, B.L.: Nonlinear acceleration of coupled fluid-structure transient thermal problems by Anderson mixing. Int. J. Numer. Methods Fluids 71(8), 939–959 (2013)

    Article  MathSciNet  Google Scholar 

  29. Gee, M., Küttler, U., Wall, W.: Truly monolithic algebraic multigrid for fluid-structure interaction. Int. J. Numer. Methods Eng. 85(8), 987–1016 (2011). DOI 10.1002/nme.3001

    Article  MATH  Google Scholar 

  30. Haelterman, R., Degroote, J., van Heule, D., Vierendeels, J.: The quasi-Newton least squares method: a new and fast secant method analyzed for linear systems. SIAM J. Numer. Anal. 47(3), 2347–2368 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  31. Haelterman, R., Degroote, J., van Heule, D., Vierendeels, J.: On the similarities between the quasi-Newton inverse least squares method and GMRes. SIAM J. Numer. Anal. 47(6), 4660–4679 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  32. Koziel, S., Bandler, J.W., Madsen, K.: Towards a regirous formulation of the space mapping technique for engineering design. In: IEEE International Symposium on Circuits and Systems, vol. 6, pp. 5605–5608. IEEE, New York (2005)

    Google Scholar 

  33. Küttler, U., Wall, W.A.: Fixed-point fluid–structure interaction solvers with dynamic relaxation. Comput. Mech. 43(1), 61–72 (2008)

    Article  MATH  Google Scholar 

  34. Küttler, U., Wall, W.A.: Vector extrapolation for strong coupling fluid-structure interaction solvers. J. Appl. Mech. 76(2), 021205 (2009)

    Article  Google Scholar 

  35. Marklund, P.O., Nilsson, L.: Simulation of airbag inflation processes using a coupled fluid structure approach. Comput. Mech. 29(4–5), 289–297 (2002)

    Article  MATH  Google Scholar 

  36. Mehl, M., Uekermann, B., Bijl, H., Blom, D.S., Gatzhammer, B., van Zuijlen, A.H.: Parallel coupling numerics for partitioned fluid-structure interaction simulations. Comput. Math. Appl. (2015)

    Google Scholar 

  37. Michler, C., van Brummelen, E.H., de Borst, R.: An interface Newton–Krylov solver for fluid–structure interaction. Int. J. Numer. Methods Fluids 47(10–11), 1189–1195 (2005)

    Article  MATH  Google Scholar 

  38. Michler, C., van Brummelen, H., de Borst, R.: An investigation of Interface-GMRES(R) for fluid–structure interaction problems with flutter and divergence. Comput. Mech. 47(1), 17–29 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  39. Ross, M.R., Felippa, C.A., Park, K., Sprague, M.A.: Treatment of acoustic fluid-structure interaction by localized Lagrange multipliers: formulation. Comput. Methods Appl. Mech. Eng. 197(33–40), 3057–3079 (2008). DOI 10.1016/j.cma.2008.02.017. URL http://linkinghub.elsevier.com/retrieve/pii/S0045782508000625

  40. Scholcz, T.P., van Zuijlen, A.H., Bijl, H.: Space-mapping in fluid-structure interaction problems. Comput. Methods Appl. Mech. Eng. 281, 162–183 (2014)

    Article  Google Scholar 

  41. Stein, K., Benney, R., Kalro, V., Tezduyar, T.E., Leonard, J., Accorsi, M.: Parachute fluid-structure interactions: 3-D computation. Comput. Methods Appl. Mech. Eng. 190(3–4), 373–386 (2000)

    Article  MATH  Google Scholar 

  42. Tezduyar, T.E., Sathe, S., Keedy, R., Stein, K.: Space–time finite element techniques for computation of fluid–structure interactions. Comput. Methods Appl. Mech. Eng. 195(17), 2002–2027 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  43. Turek, S., Hron, J.: Proposal for numerical benchmarking of fluid-structure interaction between an elastic object and laminar incompressible flow. In: Bungartz, H.J., Schäfer, M. (eds.) Fluid-Structure Interaction: Modelling, Simulation, Optimisation, vol. 53, pp. 371–385. Springer, Berlin/Heidelberg (2006)

    Chapter  Google Scholar 

  44. Uekermann, B., Bungartz, H.J., Gatzhammer, B., Mehl, M.: A parallel, black-box coupling algorithm for fluid-structure interaction. In: Proceedings of 5th International Conference on Computational Methods for Coupled Problems in Science and Engineering, pp. 1–12. Ibiza (2013)

    Google Scholar 

  45. van Brummelen, E.H.: Partitioned iterative solution methods for fluid-structure interaction. Int. J. Numer. Methods Fluids 65(1–3), 3–27 (2011)

    Article  MATH  Google Scholar 

  46. van Zuijlen, A.H., Bijl, H.: Multi-Level Accelerated Sub-Iterations for Fluid-Structure Interaction. Lecture Notes in Computational Science and Engineering, vol. 73, Chap. 1, pp. 1–25. Springer, Berlin/Heidelberg (2010)

    Google Scholar 

  47. Walker, H.F., Ni, P.: Anderson acceleration for fixed-point iterations. SIAM J. Numer. Anal. 49(4), 1715–1735 (2011)

    Article  MATH  MathSciNet  Google Scholar 

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Acknowledgement

The financial support of the Institute for Advanced Study (IAS) of the Technische Universität München, of SPPEXA, the German Science Foundation Priority Programme 1648—Software for Exascale Computing, and the Aerospace Engineering department at the Delft University of Technology is thankfully acknowledged.

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Blom, D.S., Uekermann, B., Mehl, M., van Zuijlen, A.H., Bijl, H. (2015). Multi-Level Acceleration of Parallel Coupled Partitioned Fluid-Structure Interaction with Manifold Mapping. In: Mehl, M., Bischoff, M., Schäfer, M. (eds) Recent Trends in Computational Engineering - CE2014. Lecture Notes in Computational Science and Engineering, vol 105. Springer, Cham. https://doi.org/10.1007/978-3-319-22997-3_8

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