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An added-mass free semi-implicit coupling scheme for fluid-structure interaction. (English. Abridged French version) Zbl 1156.74051
Summary: We propose a semi-implicit coupling scheme for numerical simulation of fluid-structure interaction involving a viscous incompressible fluid. The scheme is stable irrespectively of the so-called added-mass effect and allows for conservative time-stepping within the structure. The efficiency of the scheme is based on an explicit splitting of viscous effects and geometrical/convective non-linearities, through the use of Chorin-Temam projection scheme within the fluid. Stability relies on the implicit treatment of the pressure stresses and on Nitsche’s treatment of the viscous coupling.

MSC:
74S20Finite difference methods in solid mechanics
74F10Fluid-solid interactions
76D05Navier-Stokes equations (fluid dynamics)
Software:
FreeFem++
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Full Text: DOI
References:
[1] M. Astorino, F. Chouly, M.A. Fernández, An added-mass free semi-implicit coupling scheme in fluid -- structure interaction: numerical analysis and applications, in preparation · Zbl 1156.74051 · doi:10.1016/j.crma.2008.11.003
[2] Becker, R.; Hansbo, P.; Stenberg, R.: A finite element method for domain decomposition with non-matching grids, M2AN math. Model. numer. Anal. 37, No. 2, 209-225 (2003) · Zbl 1047.65099 · doi:10.1051/m2an:2003023 · numdam:M2AN_2003__37_2_209_0
[3] Burman, E.; Fernández, M. A.: Stabilized explicit coupling for fluid -- structure interaction using Nitsche’s method, C. R. Math. acad. Sci. Paris 345, No. 8, 467-472 (2007) · Zbl 1126.74047 · doi:10.1016/j.crma.2007.09.010
[4] E. Burman, M.A. Fernández, Stabilization of explicit coupling in fluid -- structure interaction involving fluid incompressibility, INRIA Research Report RR-6445, 2008, Comput. Methods Appl. Mech. Engrg., doi:10.1016/j.cma.2008.10.012, http://dx.doi.org/10.1016/j.cma.2008.10.012
[5] Causin, P.; Gerbeau, J. -F.; Nobile, F.: Added-mass effect in the design of partitioned algorithms for fluid -- structure problems, Comput. methods appl. Mech. engrg. 194, No. 42 -- 44, 4506-4527 (2005) · Zbl 1101.74027 · doi:10.1016/j.cma.2004.12.005
[6] 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. meth. Engrg. 69, No. 4, 794-821 (2007) · Zbl 1194.74393 · doi:10.1002/nme.1792
[7] , Cardiovascular mathematics 1 (2009)
[8] F. Hecht, O. Pironneau, A. Le Hyaric, K. Ohtsuka, FreeFem++ v. 2.11. User’s Manual, University of Paris 6
[9] Quaini, A.; Quarteroni, A.: A semi-implicit approach for fluid -- structure interaction based on an algebraic fractional step method, Math. models methods appl. Sci. 17, No. 6, 957-983 (2007) · Zbl 05176130