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**An adaptive remeshing strategy for flows with moving boundaries and fluid – structure interaction.**
*(English)*
Zbl 1194.76140

Summary: The primary objective of this work is to extend the capability of the arbitrary Lagrangian-Eulerian (ALE)-based strategy for solving fluid – structure interaction problems. This is driven by the fact that the ALE mesh movement techniques will not be able to treat problems in which fluid – structure interface experiences large motion. In addition, for certain problems the need arises to capture accurately flow features, such as a region with high gradients of the solution variables. This can be achieved by incorporating an adaptive remeshing procedure into the solution strategy.

The fluid flow is governed by the incompressible Navier-Stokes equations and modelled by using stabilized low order velocity pressure finite elements. The motion of the fluid domain is accounted for by an arbitrary Lagrangian-Eulerian (ALE) strategy. The flexible structure is represented by means of appropriate standard finite element formulations while the motion of the rigid body is described by rigid body dynamics. For temporal discretization of both fluid and solid bodies, the discrete implicit generalized-\(\alpha\) method is employed. The resulting strongly coupled set of nonlinear equations is then solved by means of a novel partitioned solution procedure, which is based on the Newton-Raphson methodology and incorporates full linearization of the overall incremental problem.

Within the adaptive solution strategy, the quality of fluid mesh and the solution quality indicator are evaluated regularly and compared against the appropriate remeshing criteria to decide whether a remeshing step is required. The adaptive remeshing procedure follows closely the standard computational procedure in which the adaptive remeshing process produces a mesh that can capture salient features of the flow field. For the problems under consideration in this work the motion of the fluid boundary very often results in boundaries with very high curvatures and a fluid domain that contain areas with small cross-sections. To be able to generate meshes that give result with acceptable accuracy these local geometrical features need to be included in determining the element density distribution. The numerical examples demonstrate the robustness and efficiency of the methodology.

The fluid flow is governed by the incompressible Navier-Stokes equations and modelled by using stabilized low order velocity pressure finite elements. The motion of the fluid domain is accounted for by an arbitrary Lagrangian-Eulerian (ALE) strategy. The flexible structure is represented by means of appropriate standard finite element formulations while the motion of the rigid body is described by rigid body dynamics. For temporal discretization of both fluid and solid bodies, the discrete implicit generalized-\(\alpha\) method is employed. The resulting strongly coupled set of nonlinear equations is then solved by means of a novel partitioned solution procedure, which is based on the Newton-Raphson methodology and incorporates full linearization of the overall incremental problem.

Within the adaptive solution strategy, the quality of fluid mesh and the solution quality indicator are evaluated regularly and compared against the appropriate remeshing criteria to decide whether a remeshing step is required. The adaptive remeshing procedure follows closely the standard computational procedure in which the adaptive remeshing process produces a mesh that can capture salient features of the flow field. For the problems under consideration in this work the motion of the fluid boundary very often results in boundaries with very high curvatures and a fluid domain that contain areas with small cross-sections. To be able to generate meshes that give result with acceptable accuracy these local geometrical features need to be included in determining the element density distribution. The numerical examples demonstrate the robustness and efficiency of the methodology.

### MSC:

76M10 | Finite element methods applied to problems in fluid mechanics |

76D05 | Navier-Stokes equations for incompressible viscous fluids |

74F10 | Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) |

### Keywords:

finite element; fluid-structure interaction; partitioned approach; Newton-Raphson solution method; adaptive strategy
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\textit{P. H. Saksono} et al., Int. J. Numer. Methods Eng. 71, No. 9, 1009--1050 (2007; Zbl 1194.76140)

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### References:

[1] | Ohayon, Computer Methods in Applied Mechanics and Engineering 190 pp 2977– (2001) |

[2] | Matthies, Computers and Structures 83 pp 91– (2005) |

[3] | Dettmer, Computer Methods in Applied Mechanics and Engineering 195 pp 1633– (2006) |

[4] | Dettmer, Computer Methods in Applied Mechanics and Engineering 195 pp 5754– (2006) |

[5] | Masud, Computer Methods in Applied Mechanics and Engineering 146 pp 91– (1997) |

[6] | Fluid–Struktur-Interaktion mit Stabilisierten Finiten Elementen. Ph.D. Thesis, Universität Stuttgart, 1999. |

[7] | Tezduyar, Archives of Computational Methods in Engineering 8 pp 83– (2001) |

[8] | Hübner, Computer Methods in Applied Mechanics and Engineering 193 pp 2087– (2004) |

[9] | de Sampaio, International Journal for Numerical Methods in Fluids 44 pp 673– (2004) |

[10] | Bertrand, International Journal for Numerical Methods in Fluids 25 pp 719– (1997) |

[11] | Baaijens, International Journal for Numerical Methods in Fluids 35 pp 743– (1997) |

[12] | Glowinski, Computer Methods in Applied Mechanics and Engineering |

[13] | Peskin, Acta Numerica 11 pp 479– (2002) |

[14] | Zhang, Computer Methods in Applied Mechanics and Engineering 193 pp 2051– (2004) |

[15] | Tezduyar, Computer Methods in Applied Mechanics and Engineering 95 pp 221– (1992) |

[16] | Jansen, Computer Methods in Applied Mechanics and Engineering 190 pp 305– (2000) |

[17] | Dettmer, Computer Methods in Applied Mechanics and Engineering 192 pp 1177– (2003) |

[18] | Kalro, Computer Methods in Applied Mechanics and Engineering 190 pp 321– (2000) |

[19] | Stein, Computer Methods in Applied Mechanics and Engineering 191 pp 673– (2001) |

[20] | Matthies, Computers and Structures 80 pp 1991– (2002) |

[21] | Matthies, Computers and Structures 81 pp 805– (2003) |

[22] | Fernández, Computers and Structures 83 pp 127– (2003) |

[23] | Heil, Computer Methods in Applied Mechanics and Engineering 193 pp 1– (2004) |

[24] | Finite element modelling of fluid flow with moving free surfaces and interfaces including fluid–solid interaction. Ph.D. Thesis, University of Wales Swansea, U.K., 2004. |

[25] | Dettmer, Computer Methods in Applied Mechanics and Engineering 195 pp 3038– (2006) |

[26] | Bach, Journal of Fluid Mechanics 152 pp 173– (1985) |

[27] | Masud, Computers and Fluids 36 pp 77– (2007) |

[28] | Saksono, Computational Mechanics 38 pp 251– (2006) |

[29] | Wu, Computational Mechanics 6 pp 259– (1990) |

[30] | Hétu, AIAA Journal 30 pp 2677– (1992) |

[31] | Prudhomme, Finite Elements in Analysis Design 33 pp 247– (1999) |

[32] | Oñate, Computer Methods in Applied Mechanics and Engineering 195 pp 339– (2006) |

[33] | Lee, International Journal for Numerical Methods in Engineering 50 pp 787– (2001) |

[34] | Erhart, International Journal for Numerical Methods in Engineering 65 pp 2139– (2006) |

[35] | Perić, Computer Methods in Applied Mechanics and Engineering 137 pp 331– (1996) |

[36] | Perić, Computer Methods in Applied Mechanics and Engineering 176 pp 279– (1999) |

[37] | . Computational modelling of forming processes. In Encyclopaedia of Computational Mechanics. Volume 2: Solids and Structures, , (eds). Wiley: Chichester, 2004; 461–511. |

[38] | Perić, Computer Methods in Applied Mechanics and Engineering 193 pp 5195– (2004) |

[39] | , . Nonlinear Finite Elements for Continua and Structures. Wiley: Chichester, 2000. · Zbl 0959.74001 |

[40] | . Finite Element Methods for Flow Problems. Wiley: Chichester, 2003. |

[41] | , , . Computational unsteady incompressible flows with the stabilized finite element methods–space-time formulations. Iterative strategies and massively parallel implementations. New Methods in Transient Analysis, vol. 143. AMD: New York, 1992; 7–24. |

[42] | Johnson, Computer Methods in Applied Mechanics and Engineering 119 pp 73– (1994) |

[43] | Bar-Yoseph, Computational Mechanics 27 pp 378– (2001) |

[44] | Degan, Computers and Structures 80 pp 305– (2002) |

[45] | Brooks, Computer Methods in Applied Mechanics and Engineering 32 pp 199– (1982) |

[46] | Tezduyar, Computer Methods in Applied Mechanics and Engineering 190 pp 411– (2000) |

[47] | Oñate, Computer Methods in Applied Mechanics and Engineering 182 pp 355– (2000) |

[48] | Braess, Computer Methods in Applied Mechanics and Engineering 190 pp 95– (2000) |

[49] | Ramaswamy, Journal of Computational Physics 90 pp 396– (1990) |

[50] | Hughes, Computer Methods in Applied Mechanics and Engineering 73 pp 173– (1989) |

[51] | Chung, Journal of Applied Mechanics 60 pp 371– (1993) |

[52] | , , . Space–time techniques for finite element computation of flows with moving boundaries and interfaces. Proceedings of the III International Congress on Numerical Methods in Engineering and Applied Sciences, Monterry, Mexico, 2004; CD-ROM. |

[53] | Tezduyar, International Journal for Numerical Methods in Engineering 195 pp 2002– (2006) |

[54] | Tezduyar, Computational Mechanics 18 pp 397– (1996) |

[55] | Behr, Computer Methods in Applied Mechanics and Engineering 174 pp 261– (1999) |

[56] | Behr, Computer Methods in Applied Mechanics and Engineering 190 pp 3189– (2001) |

[57] | Johnson, Computer Methods in Applied Mechanics and Engineering 134 pp 351– (1996) |

[58] | Johnson, Computer Methods in Applied Mechanics and Engineering 145 pp 301– (1997) |

[59] | Glowinski, International Journal of Multiphase Flow 25 pp 755– (1999) |

[60] | Patankar, International Journal of Multiphase Flow 26 pp 1509– (2000) |

[61] | Wagner, International Journal for Numerical Methods in Engineering 51 pp 293– (2001) |

[62] | , (eds). Perry’s Chemical Engineering Handbook. McGraw-Hill: New York, 1999. |

[63] | Ceylan, Powder Technology 119 pp 250– (2001) |

[64] | Zhang, Journal of Applied Mechanics 70 pp 64– (2003) |

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.