我们推导了用于具有接触的流固耦合（FSI）问题的基于Nitsche的公式。该方法基于Chouly和Hild [SIAM Journal on Numerical Analysis. 2013;51(2):1295--1307] 对固体力学接触问题的工作。我们提出了两种数值方法，两者均在联合界面-接触表面Γ(t)上以方程形式同时公式化FSI界面和接触条件。第一种方法通过放松接触条件，允许固体和壁之间存在小的网格依赖间隙。第二种方法在接触表面下方引入人工流体。所得到的方程组可以一致地包含在单块变分公式中，从而防止所谓的'颤振'现象。为处理流体域在撞击时刻的拓扑变化，我们使用全欧拉方法处理FSI问题。我们比较了滑动和无滑动界面条件的效果，并通过数值实验研究了该方法的性能。
英文摘要：
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 Journal on Numerical Analysis. 2013;51(2):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 $Γ(t)$. 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.
Skew-symmetric Nitsche's formulation in isogeometric analysis: Dirichlet and symmetry conditions, patch coupling and frictionless contact
Dalian University of Technology（大连理工大学）；University of Luxembourg（卢森堡大学）；Université Bourgogne Franche-Comté（勃艮第-弗朗什-孔泰大学）；Cardiff University（卡迪夫大学）；University of Western Australia（西澳大学）
A Nitsche method for incompressible fluids with general dynamic boundary conditions
Charles University（查理大学）；Universität Konstanz（康斯坦茨大学）；Institute of Science and Technology Austria (ISTA)（奥地利科学技术研究所）；Technische Universität Darmstadt（达姆施塔特工业大学）
A Nitsche method for Navier--Stokes/generalized poroelasticity interface problems
Indian Institute of Technology Roorkee（印度理工学院鲁尔基分校）；Pontificia Universidad Católica de Chile（智利天主教公立大学）；Centro de Modelamiento Matemático (CNRS IRL2807)（数学建模中心（法国国家科学研究中心国际研究联络处2807））；Monash University（蒙纳士大学）；Universidad Adventista de Chile（智利基督复临安息日会大学）
A Unified-Field Monolithic Fictitious Domain-Finite Element Method for Fluid-Structure-Contact Interactions and Applications to Deterministic Lateral Displacement Problems
A numerical benchmark for fluid--structure--contact interaction
Mathematical Institute, Faculty of Mathematics and Physics, Charles University（查理大学数学物理学院数学研究所）；University of Konstanz, Department of Mathematics & Statistics（康斯坦茨大学数学与统计系）；Leibniz University Hannover, Institute of Applied Mathematics（汉诺威莱布尼茨大学应用数学研究所）；Department of Mathematical Analysis, Faculty of Mathematics and Physics, Charles University（查理大学数学物理学院数学分析系）；Department of Mathematics, Uppsala University（乌普萨拉大学数学系）
Analysis and Simulation of a Fluid-Heat System in a Thin, Rough Layer in Contact With a Solid Bulk Domain
Center for Industrial Mathematics, University of Bremen, Germany（不来梅大学工业数学中心）；Faculty of Mathematics, University Regensburg, Germany（雷根斯堡大学数学系）；Mathematics Department, Karlstad University, Sweden（卡尔斯塔德大学数学系）
A Mortar Finite Element Formulation for Large Deformation Lubricated Contact Problems with Smooth Transition Between Mixed, Elasto-Hydrodynamic and Full Hydrodynamic Lubrication
