The enriched space–time finite element method (EST) for simultaneous solution of fluid–structure interaction

International audienceThe paper introduces a weighted residual-based approach for the numerical investigation of the interaction of fluid flow and thin flexible structures. The presented method enables one to treat strongly coupled systems involving large structural motion and deformation of multiple-flow-immersed solid objects. The fluid flow is described by the incompressible Navier–Stokes equations. The current configuration of the thin structure of linear elastic material with non-linear kinematics is mapped to the flow using the zero iso-contour of an updated level set function. The formulation of fluid, structure and coupling conditions uniformly uses velocities as unknowns. The integration of the weak form is performed on a space–time finite element discretization of the domain. Interfacial constraints of the multi-field problem are ensured by distributed Lagrange multipliers. The proposed formulation and discretization techniques lead to a monolithic algebraic system, well suited for strongly coupled fluid–structure systems. Embedding a thin structure into a flow results in non-smooth fields for the fluid. Based on the concept of the extended finite element method, the space–time approximations of fluid pressure and velocity are properly enriched to capture weakly and strongly discontinuous solutions. This leads to the present enriched space–time (EST) method. Numerical examples of fluid–structure interaction show the eligibility of the developed numerical approach in order to describe the behavior of such coupled systems. The test cases demonstrate the application of the proposed technique to problems where mesh moving strategies often fail

Efficient simulation of blood flow past complex endovascular devices using an adaptive embedding technique

The simulation of blood flow past endovascular devices such as coils and stents is a challenging problem due to the complex geometry of the devices. Traditional unstructured grid computational fluid dynamics relies on the generation of finite element grids that conform to the boundary of the computational domain. However, the generation of such grids for patient-specific modeling of cerebral aneurysm treatment with coils or stents is extremely difficult and time consuming. This paper describes the application of an adaptive grid embedding technique previously developed for complex fluid structure interaction problems to the simulation of endovascular devices. A hybrid approach is used: the vessel walls are treated with body conforming grids and the endovascular devices with an adaptive mesh embedding technique. This methodology fits naturally in the framework of image-based computational fluid dynamics and opens the door for exploration of different therapeutic options and personalization of endovascular procedures

A Nitsche-based cut finite element method for a fluid--structure interaction problem

We present a new composite mesh finite element method for fluid--structure interaction problems. The method is based on surrounding the structure by a boundary-fitted fluid mesh which is embedded into a fixed background fluid mesh. The embedding allows for an arbitrary overlap of the fluid meshes. The coupling between the embedded and background fluid meshes is enforced using a stabilized Nitsche formulation which allows us to establish stability and optimal order \emph{a priori} error estimates, see~\cite{MassingLarsonLoggEtAl2013}. We consider here a steady state fluid--structure interaction problem where a hyperelastic structure interacts with a viscous fluid modeled by the Stokes equations. We evaluate an iterative solution procedure based on splitting and present three-dimensional numerical examples.Comment: Revised version, 18 pages, 7 figures. Accepted for publication in CAMCo

Weakly Enforced Boundary Conditions for the NURBS-Based Finite Cell Method

In this paper, we present a variationally consistent formulation for the weak enforcement of essential boundary conditions as an extension to the finite cell method, a fictitious domain method of higher order. The absence of boundary fitted elements in fictitious domain or immersed boundary methods significantly restricts a strong enforcement of essential boundary conditions to models where the boundary of the solution domain coincides with the embedding analysis domain. Penalty methods and Lagrange multiplier methods are adequate means to overcome this limitation but often suffer from various drawbacks with severe consequences for a stable and accurate solution of the governing system of equations. In this contribution, we follow the idea of NITSCHE [29] who developed a stable scheme for the solution of the Laplace problem taking weak boundary conditions into account. An extension to problems from linear elasticity shows an appropriate behavior with regard to numerical stability, accuracy and an adequate convergence behavior. NURBS are chosen as a high-order approximation basis to benefit from their smoothness and flexibility in the process of uniform model refinement

Grid adaption using Chimera composite overlapping meshes

The objective of this paper is to perform grid adaptation using composite over-lapping meshes in regions of large gradient to capture the salient features accurately during computation. The Chimera grid scheme, a multiple overset mesh technique, is used in combination with a Navier-Stokes solver. The numerical solution is first converged to a steady state based on an initial coarse mesh. Solution-adaptive enhancement is then performed by using a secondary fine grid system which oversets on top of the base grid in the high-gradient region, but without requiring the mesh boundaries to join in any special way. Communications through boundary interfaces between those separated grids are carried out using tri-linear interpolation. Applications to the Euler equations for shock reflections and to a shock wave/boundary layer interaction problem are tested. With the present method, the salient features are well resolved

Effects of an embedding bulk fluid on phase separation dynamics in a thin liquid film

Using dissipative particle dynamics simulations, we study the effects of an embedding bulk fluid on the phase separation dynamics in a thin planar liquid film. The domain growth exponent is altered from 2D to 3D behavior upon the addition of a bulk fluid, even though the phase separation occurs in 2D geometry. Correlated diffusion measurements in the film show that the presence of bulk fluid changes the nature of the longitudinal coupling diffusion coefficient from logarithmic to algebraic dependence of 1/s, where s is the distance between the two particles. This result, along with the scaling exponents, suggests that the phase separation takes place through the Brownian coagulation process.Comment: 6 pages, 5 figures. Accepted for publication in Europhys. Let