A Unified Arbitrary Lagrangian-Eulerian Model for Fluid-Structure Interaction Problems Involving Flows in Flexible Channels

In this work a finite element-based model for analyzing incompressible flows in flexible channels is presented. The model treats the fluid-solid interaction problem in a monolithic way, where the governing equations for both sub-domains are solved on a single moving grid taking advantage of an arbitrary Lagrangian/Eulerian framework (ALE). The unified implementation of the governing equations for both sub-domains is developed, where these are distinguished only in terms of the mesh-moving strategy and the constitutive equation coefficients. The unified formulation is derived considering a Newtonian incompressible fluid and a hypoelastic solid. Hypoelastic constitutive law is based on the strain rate and thus naturally facilitates employing velocity as a kinematic variable in the solid. Unifying the form of the governing equations and defining a semi-Lagrangian interface mesh-motion algorithm, one obtains the coupled problem formulated in terms of a unique kinematic variable. Resulting monolithic system is characterized by reduced variable heterogeneity resembling that of a single-media problem. The model used in conjunction with algebraic multigrid linear solver exhibits attractive convergence rates. The model is tested using a 2D and a 3D example.

Automated summary

A finite element-based model for analyzing incompressible flows in flexible channels is presented in this work. The model treats the fluid-solid interaction problem in a monolithic way, using an arbitrary Lagrangian/Eulerian framework. The governing equations for both sub-domains are solved on a single moving grid, with the mesh-moving strategy and the constitutive equation coefficients as the distinguishing factors. The unified formulation of the governing equations and the use of a semi-Lagrangian interface mesh-motion algorithm result in a coupled problem formulated in terms of a unique kinematic variable. The model exhibits high convergence rates when used with an algebraic multigrid linear solver.