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
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页码:531 / 564
页数:34
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