A Nitsche-based formulation for fluid-structure interactions with contact

被引:34
|
作者
Burman, Erik [1 ]
Fernandez, Miguel A. [2 ,3 ,4 ]
Frei, Stefan [1 ]
机构
[1] UCL, Dept Math, Gower St, London WC1E 6BT, England
[2] Inria Paris, F-75012 Paris, France
[3] Sorbonne Univ, F-75005 Paris, France
[4] CNRS, UMR 7598, LJLL, F-75005 Paris, France
来源
ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE | 2020年 / 54卷 / 02期
基金
英国工程与自然科学研究理事会;
关键词
Fluid-structure interaction; contact mechanics; Eulerian formalism; Nitsche's method; slip conditions; FINITE-ELEMENT-METHOD; ACTIVE SET STRATEGY; FRICTIONAL CONTACT; INCOMPRESSIBLE FLUID; EULERIAN FORMULATION; STOKES PROBLEM; APPROXIMATION; DYNAMICS; MODELS; DISCRETIZATION;
D O I
10.1051/m2an/2019072
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We derive a Nitsche-based formulation for fluid-structure interaction (FSI) problems with contact. The approach is based on the work of Chouly and Hild (SIAM J. Numer. Anal. 51 (2013) 1295-1307) for contact problems in solid mechanics. We present two numerical approaches, both of them formulating the FSI interface and the contact conditions simultaneously in equation form on a joint interface-contact surface Gamma(t). The first approach uses a relaxation of the contact conditions to allow for a small mesh-dependent gap between solid and wall. The second alternative introduces an artificial fluid below the contact surface. The resulting systems of equations can be included in a consistent fashion within a monolithic variational formulation, which prevents the so-called "chattering" phenomenon. To deal with the topology changes in the fluid domain at the time of impact, we use a fully Eulerian approach for the FSI problem. We compare the effect of slip and no-slip interface conditions and study the performance of the method by means of numerical examples.
引用
收藏
页码:531 / 564
页数:34
相关论文
共 50 条
  • [21] An unfitted Nitsche method for incompressible fluid-structure interaction using overlapping meshes
    Burman, Erik
    Fernandez, Miguel A.
    COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2014, 279 : 497 - 514
  • [22] MATHEMATICAL FORMULATION OF FLUID-STRUCTURE INTERACTION PROBLEMS
    BOUJOT, J
    RAIRO-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE, 1987, 21 (02): : 239 - 260
  • [23] ALE formulation for fluid-structure interaction problems
    Souli, M
    Ouahsine, A
    Lewin, L
    COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2000, 190 (5-7) : 659 - 675
  • [24] Numerical Study of a Monolithic Fluid-Structure Formulation
    Pironneau, Olivier
    VARIATIONAL ANALYSIS AND AEROSPACE ENGINEERING: MATHEMATICAL CHALLENGES FOR THE AEROSPACE OF THE FUTURE, 2016, 116 : 401 - 420
  • [25] On monolithic approaches to fluid-structure interactions
    Etienne, S
    Pelletier, D
    Tremblay, D
    Garon, A
    Fluid Structure Interaction and Moving Boundary Problems, 2005, 84 : 339 - 349
  • [26] BENCHMARK PROBLEMS FOR FLUID-STRUCTURE INTERACTIONS
    TAKEUCHI, K
    YOUNGDAHL, CK
    TRANSACTIONS OF THE AMERICAN NUCLEAR SOCIETY, 1981, 39 : 478 - 481
  • [27] A Nitsche-based domain decomposition method for hypersingular integral equations
    Chouly, Franz
    Heuer, Norbert
    NUMERISCHE MATHEMATIK, 2012, 121 (04) : 705 - 729
  • [28] An Eulerian shell formulation for fluid-structure interaction
    Benson, DJ
    Stainier, L
    COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2000, 187 (3-4) : 571 - 590
  • [29] A SYMMETRIC POTENTIAL FORMULATION FOR FLUID-STRUCTURE INTERACTION
    EVERSTINE, GC
    JOURNAL OF SOUND AND VIBRATION, 1981, 79 (01) : 157 - 160
  • [30] NUMERICAL MODELLING OF FLUID-STRUCTURE INTERACTIONS
    Fortin, A.
    Jendoubi, A.
    Deteix, J.
    Coupled Problems in Science and Engineering VI, 2015, : 1138 - 1146