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

Abstract

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.

A consistent approach for fluid‐structure‐contact interaction based on a porous flow model for rough surface contact

“…Condition (26) guarantees that there is always a positive gap or no gap between potentially contacting bodies. Additionally, (27) restricts the minimal stress by compression transferred directly between the solid bodies to the surrounding fluid normal traction. Herein, h I (eg, h I = P · n P + p P n P [available on Γ PS,c and Γ FP ] or h I = S · n P − F · n P [available on Γ FS ]) is the traction difference between the total contact traction and the ambient fluid stress.…”

“…To compute the traction difference h I , which is required to formulate condition (27), the physical model has to provide a reliable fluid traction on the overall interface Γ. This is especially critical in the contacting zone Γ PS,c .…”

“…Then, for the normal components of velocity and normal traction difference, the following relations hold. = 0 transition point of (27) = n · P · n + p P condition (24) = n · S · n + p P…”

“…It should be pointed out that for a pure structural contact case with vanishing fluid, conditions (26), (27), and (28) reduce to the classical contact conditions, as the relative traction is equal to the absolute traction for vanishing fluid pressure.…”

Space–time adaptive finite elements for nonlocal parabolic variational inequalities

“…For local differential equations, the pure and numerical analysis of variational inequalities has a long history [51], especially motivated by contact problems in mechanics [42,44,61]. Of particular current interest in numerical analysis have been dynamic contact problems for time-dependent equations, including adaptive mesh refinements [40,43], high-order [8] and Nitsche methods [19,23]. Their analysis is crucial for applications from tire dynamics [7,40] to blood flow in aortic valves [4].…”