## On the coupling between fluid flow and mesh motion in the modelling of fluid-structure interaction.(English)Zbl 1235.74272

Summary: Partitioned Newton type solution strategies for the strongly coupled system of equations arising in the computational modelling of fluid-solid interaction require the evaluation of various coupling terms. An essential part of all ALE type solution strategies is the fluid mesh motion. In this paper, we investigate the effect of the terms which couple the fluid flow with the fluid mesh motion on the convergence of the overall solution procedure. We show that the computational efficiency of the simulation of many fluid-solid interaction processes, including fluid flow through flexible pipes, can be increased significantly if some of these coupling terms are calculated exactly.

### MSC:

 74S05 Finite element methods applied to problems in solid mechanics 74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) 76M10 Finite element methods applied to problems in fluid mechanics 76D05 Navier-Stokes equations for incompressible viscous fluids
Full Text:

### References:

 [1] Bazilevs Y (2007) private communication [2] Brooks AN, Hughes TJR (1982) Streamline-upwind/Petrov– Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier–Stokes equations. Comput Meth Appl Mech Eng 32: 199–259 · Zbl 0497.76041 [3] Chung J, Hulbert GM (1993) A time integration algorithm for structural dynamics with improved numerical dissipation: the generalized-{$$\alpha$$} method. J Appl Mech 60: 371–375 · Zbl 0775.73337 [4] Dettmer WG, Perić D (2003) An analysis of the time integration algorithms for the finite element solutions of incompressible Navier–Stokes equations based on a stabilised formulation. Comput Meth Appl Mech Eng 192: 1177–1226 · Zbl 1091.76521 [5] Dettmer WG, Perić D (2006) A computational framework for fluid-structure interaction: finite element formulation and applications. Comput Meth Appl Mech Eng 195: 5754–5779 · Zbl 1155.76354 [6] Dettmer WG, Perić D (2006) A computational framework for fluid–rigid body interaction: finite element formulation and applications. Comput Meth Appl Mech Eng 195: 1633–1666 · Zbl 1123.76029 [7] Dettmer WG, Perić D (2006) A computational framework for free surface fluid flows accounting for surface tension. Comput Meth Appl Mech Eng 195: 3038–3071 · Zbl 1115.76043 [8] Dettmer WG, Peric D (2007) A fully implicit computational strategy for strongly coupled fluid–solid interaction. Arch Comput Method Eng 14(3): 205–247 · Zbl 1160.74044 [9] Farhat C, Lesoinne M, Le Tallec P (1998) Load and motion transfer algorithms for fluid/structure interaction problems with non-matching discrete interfaces: momentum and energy conservation, optimal discretisation and application to aeroelasticity. Comput Meth Appl Mech Eng 157: 95–114 · Zbl 0951.74015 [10] Felippa CA, Park KC, Farhat C (2001) Partitioned analysis of coupled mechanical systems. Comput Meth Appl Mech Eng 190: 3247–3270 · Zbl 0985.76075 [11] Fernandez MA, Moubachir A (2005) A Newton method using exact Jacobians for solving fluid structure coupling. Comput Struct 83(2–3): 127–142 [12] Heil M (2004) An efficient solver for the fully coupled solution of large-displacement fluid–structure interaction problems. Comput Meth Appl Mech Eng 193: 1–23 · Zbl 1137.74439 [13] Hughes TJR, Franca LP, Hulbert GM (1989) A new finite element formulation for computational fluid dynamics: VIII. The Galerkin/least-squares method for advective-diffusive equations. Comput Meth Appl Mech Eng 73: 173–189 · Zbl 0697.76100 [14] Hughes TJR, Franca LP, Balestra M (1986) A new finite element formulation for computational fluid dynamics: V. Circumventing the Babuska–Brezzi condition: a stable Petrov–Galerkin formulation of the Stokes problem accommodating equal-order interpolations. Comput Meth Appl Mech Eng 59: 85–99 · Zbl 0622.76077 [15] Jansen KE, Whiting CH, Hulbert GM (2000) A generalized {$$\alpha$$}-method for integrating the filtered Navier–Stokes equations with a stabilized finite element method. Comput Meth Appl Mech Eng 190: 305–319 · Zbl 0973.76048 [16] Kalro V, Tezduyar TE (2000) A parallel 3D computational method for fluid–structure interactions in parachute systems. Comput Meth Appl Mech Eng 190: 321–332 · Zbl 0993.76044 [17] Küttler U, Förster Ch, Wall WA (2006) A solution for the incompressibility dilemma in partitioned fluid–structure interaction with pure dirichlet fluid domains. Comput Mech 38: 417–429 · Zbl 1166.74046 [18] Matthies HG, Steindorf J (2002) Partitioned but strongly coupled iteration schemes for nonlinear fluid–structure interaction. Comput Struct 80: 1991–1999 [19] Matthies HG, Steindorf J (2003) Partitioned strong coupling algorithms for fluid–structure interaction. Comput Struct 81: 805–812 [20] Matthies HG, Niekamp R, Steindorf J (2006) Algorithms for strong coupling procedures. Comput Meth Appl Mech Eng 195: 2028–2049 · Zbl 1142.74050 [21] Mittal S, Tezduyar TE (1995) Parallel finite element simulation of 3D incompressible flows–fluid–structure interactions. Int J Numer Method Fluid 21: 933–953 · Zbl 0873.76047 [22] Pedley TJ, Stephanoff KD (1985) Flow along a channel with a time-dependent indentation in one wall: the generation of vorticity waves. J Fluid Mech 160: 337–367 [23] Robertson I, Sherwin SJ, Bearman PW (2003) A numerical study of rotational and transverse galloping rectangular bodies. J Fluid Struct 17: 681–699 [24] Saksono PH, Dettmer WG, Perić D (2007) An adaptive remeshing strategy for flows with moving boundaries and fluid–structure interaction. Int J Numer Method Eng 71(9): 1009–1050 · Zbl 1194.76140 [25] Tezduyar TE, Mittal S, Ray SE, Shih R (1992) Incompressible flow computations with stabilized bilinear and linear equal-order-interpolation velocity-pressure elements. Comput Meth Appl Mech Eng 95: 221–242 · Zbl 0756.76048 [26] Tezduyar TE (2001) Finite element methods for flow problems with moving boundaries and interfaces. Arch Comput Method Eng 8: 83–130 · Zbl 1039.76037 [27] Tezduyar TE, Sathe S, Keedy R, Stein K (2006) Space–time finite element techniques for computation of fluid–structure interaction. Comput Meth Appl Mech Eng 195: 2002–2027 · Zbl 1118.74052 [28] Tezduyar TE, Sathe S, Stein K (2006) Solution techniques for the fully discretized equations in computation of fluid–structure interactions with the space–time formulations. Comput Meth Appl Mech Eng 195: 5743–5753 · Zbl 1123.76035 [29] Tezduyar TE (2007) Finite elements in fluids: stabilized formulations and moving boundaries and interfaces. Comput Fluids 36: 191–206 · Zbl 1177.76202 [30] Tezduyar TE, Sathe S (2007) Modeling of fluid–structure interactions with space–time finite elements: solution techniques. Int J Numer Method Fluid 54: 855–900 · Zbl 1144.74044 [31] Wall WA (1999) Fluid-struktur interaktion mit stabilisierten finiten elementen. Ph.D. thesis, Universität Stuttgart, Germany
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.