A comparison of one-way and two-way coupling methods for numerical analysis of fluid-structure interactions. (English) Zbl 1334.74094

Benra, Friedrich-Karl; Dohmen, Hans Josef; Pei, Ji; Schuster, Sebastian; Wan, Bo

J. Appl. Math. 2011, Article ID 853560, 16 p. (2011).

Summary: The interaction between fluid and structure occurs in a wide range of engineering problems. The solution for such problems is based on the relations of continuum mechanics and is mostly solved with numerical methods. It is a computational challenge to solve such problems because of the complex geometries, intricate physics of fluids, and complicated fluid-structure interactions. The way in which the interaction between fluid and solid is described gives the largest opportunity for reducing the computational effort. One possibility for reducing the computational effort of fluid-structure simulations is the use of one-way coupled simulations. In this paper, different problems are investigated with one-way and two-way coupled methods. After an explanation of the solution strategy for both models, a closer look at the differences between these methods will be provided, and it will be shown under what conditions a one-way coupling solution gives plausible results.

MSC:

74S30	Other numerical methods in solid mechanics (MSC2010)
74F10	Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)

References:

[1]	O. C. Zienkiewicz and R. L. Taylor, The Finite Element Method, vol. 1, Butterworth-Heinemann, 5th edition, 2000. · Zbl 0991.74004
[2]	M. Schäfer, G. Sieber, R. Sieber, and I. Teschauer, “Coupled fluid-solid problems: examples and reliable numerical simulation,” in Proceedings of the Trend in Computational Structural Mechanics, International Center for Numerical Methods in Engineering (CIMNE), Barcelona, Spain, May 2001. · Zbl 1153.76388
[3]	K. C. Park, C. A. Felippa, and J. A. DeRuntz, “Stabilization of staggered solution procedures for fluid-structure interaction analysis,” in Computational Methods for Fluid-Structure Interaction Problems, T. Belytschko and T. L. Geers, Eds., vol. 26, pp. 95-124, American Society of Mechanical Engineers, New York, NY, USA, 1977. · Zbl 0389.76002
[4]	C. A. Felippa and K. C. Park, “Staggered transient analysis procedures for coupled mechanical systems: formulation,” Computer Methods in Applied Mechanics and Engineering, vol. 24, no. 1, pp. 61-111, 1980. · Zbl 0453.73091
[5]	S. Piperno, C. Farhat, and B. Larrouturou, “Partitioned procedures for the transient solution of coupled aeroelastic problems, part I: model problem, theory and two-dimensional application,” Computer Methods in Applied Mechanics and Engineering, vol. 124, no. 1-2, pp. 79-112, 1995. · Zbl 1067.74521
[6]	S. Piperno, “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, vol. 25, no. 10, pp. 1207-1226, 1997. · Zbl 0910.76065
[7]	D. P. Mok, W. A. Wall, and E. Ramm, “Accelerated iterative substructuring schemes for instationary fluid structure interaction,” in Computational Fluid and Solid Mechanics, K. J. Bathe, Ed., pp. 1325-1328, Elsevier, 2001.
[8]	F. Nobile, Numerical approximation of fluid structure interaction problems with application to haemodynamics, Ph.D. thesis, EPFL, Switzerland, 2001.
[9]	D. Peric and W. G. Dettmer, “A computational strategy for interaction of fluid flow with spatial structures,” in Proceedings of the 5th International Conference on Computational of Shell & Spatial Structures (IASS IACM ’05), 2005.
[10]	A. Timperi, “Fluid-structure interaction calculations using a linear perturbation method,” in Proceedings of the 20th International Conference on Structural Mechanics in Reactor Technology (SMiRT ’09), 2009.
[11]	J.-M. Vaassen, P. DeVincenzo, C. Hirsch, and B. Leonard, “Strong coupling algorithm to solve fluid-structure-interaction problems with a staggered approach,” in Proceedings of the 11th International WS on Simulation & EGSE Facilities for Space Programmes (SESP ’10), 2010.
[12]	A. Pozarlik and J. Kok, “Numerical investigation of one- and two-way fluid-structure interaction in combustion systems,” in Proceedings of the International Conference on Computational Methods for Coupled Problems in Science and Engineering, 2007.
[13]	M. Münsch and M. Breuer, “Numerical simulation of fluid-structure interaction using eddy-resolving schemes,” in Fluid Structure Interaction II, H.-J. Bungartz, M. Mehl, and M. Schäfer, Eds., Lecture Notes in Computational Science and Engineering, pp. 221-254, Springer, Berlin, Germany, 2010. · Zbl 1210.76114
[14]	W. Wall, Fluid-struktur interaktion mit stabilisierten finiten elemente, Dissertation, Stuttgart, Germany, 1999.
[15]	E. Walhorn, Ein simulatenes berechnungsverfahren für fluid-struktur-wechselwirkung mit finiten raum-zeit-elementen, Dissertation, Braunschweig, Germany, 2002.
[16]	J. Steindorf, Partitionierte verfahren für probleme der fluid-struktur wechselwirkung, Dissertation, Braunschweig, Germany, 2002.
[17]	RITZ Pumpenfabrik GmbH & Co. KG, “Kanalradpumpe 38,” 2011, http://www.ritz-pumpen.de/.
[18]	F.-K. Benra and H. J. Dohmen, “Investigation on the time-variant flow in a single-blade centrifugal pump,” in Proceedings of the 5th WSEAS International Conference on Fluid Mechanics (FLUIDS ’08), Acapulco, Mexico, January 2008.
[19]	F.-K. Benra and H. J. Dohmen, “Numerical and experimental evaluation of the time-variant flow field in a single-blade centrifugal pump,” in Proceedings of the 5th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics (HEFAT ’07), pp. 1-4, Sun City, South Africa, July 2007.
[20]	F.-K. Benra, H. J. Dohmen, and M. Sommer, “Flow field visualization of a single-blade centrifugal pump using PIV-method-comparison to numerical results,” Journal of Visualization, vol. 9, no. 4, p. 358, 2006.
[21]	F.-K. Benra and N. Savilius, “Experimental determination of the hydrodynamic imbalance of a single-blade centrifugal pump,” WSEAS Transactions on Fluid Mechanics, vol. 1, no. 6, pp. 707-713, 2006.
[22]	F.-K. Benra and N. Savilius, “Experimental investigation of transient hydrodynamic forces of a single-blade centrifugal pump,” in Proceedings of the 4th WSEAS International Conference on Fluid Mechanics and Aerodynamics, Crete Island, Greece, August 2006.
[23]	F.-K. Benra, “Numerical and experimental investigation on the flow induced oscillations of a single-blade pump impeller,” Journal of Fluids Engineering, vol. 128, no. 4, pp. 783-793, 2006.