Numerical simulation of interaction between incompressible flow and an elastic wall

Abstract

The present paper is devoted to the numerical solution to flow in time-dependent domains with elastic walls. This problem has several applications in engineering and medicine.  The flow is described by the system of Navier-Stokes equations supplemented with suitable initial and boundary conditions. A part of the boundary of the region occupied by the fluid is represented by an elastic wall, whose deformation is driven by a hyperbolic partial differential equation with initial and boundary conditions. Its right-hand side represents the force by which the fluid flow acts on the elastic wall. A numerical method for solving this coupled problem is elaborated, based on the finite element method and the arbitrary Lagrangian-Eulerian (ALE) formulation of the equations describing the flow. The formulation and analysis of the problem together with discretization, algorithmization and programming of modules, which were added to an existing software package, is presented. The developed method is applied to solving test problems.