A 2D stochastic nonlinearly coupled fluid-structure interaction problem in compliant arteries with unrestricted structural displacement

Abstract

In this paper, we study a nonlinear fluid-structure interaction (FSI) problem driven by a multiplicative, white-in-time noise. The problem consists of the Navier-Stokes equations describing the flow of an incompressible, viscous fluid in a 2D cylinder interacting with an elastic wall whose elastodynamics is described by membrane/shell equations. The stochastic force is applied both to the fluid equations as a volumetric body force, and to the structure as an external forcing to the deformable fluid boundary. The fluid and the structure are nonlinearly coupled via the kinematic and dynamic conditions assumed at the moving interface, which is a random variable not known a priori. Majority of the existing FSI literature builds on the assumption that the structure can only be deformed radially, neglecting its longitudinal displacement. In this article, we consider the case where the structure is allowed to have vectorial (unrestricted) deformations.