An Immerse domain method for fluid-structure interaction with contact

Overview

Abstract

We present an embedded approach for the numerical simulation of fluid-structure interaction problems. This work focuses on problems where the elastic structures undergo large deformations. Motivating applications are (1) the study of liquid diaphragm pumps used for digital inkjet printing and (2) the study of bio-prosthetic heart valves.

In both applications, we assume that the fluid is Newtonian, and we solve a series of contact problems. First, we solve the contact interaction between the different immersed structures. Second, we constrain the movement of such structures to the fluid domain. This constrained motion is required when dealing with prestressed elastic materials. This setting gives rise to a large-scale nonlinear problem which is both challenging, from an optimization point of view, and computationally expensive.

Another important aspect is dealing with moving geometries and dynamic interactions between the different bodies in distributed memory environments. Such interactions include coupling conditions between solid and fluid and the contact conditions between structure surfaces potentially in contact.
Our approach employs a parallel-tree search algorithm for assembling the coupling and contact conditions in combination with a fictitious domain approach. In particular, we employ a localized version of the $L^2$-projection for handling the fluid-structure volumetric coupling and a variant of the mortar method for coupling the surfaces of the different structures in contact.

Our strategy is verified through numerical benchmarks and finally employed to model the dynamics of liquid diaphragm pumps and a bio-prosthetic heart valve placed in the aortic root.

Brief Biography

Dr. Patrick Zulian, is a scientific collaborator in the group of Prof. Rolf Krause at the Euler institute (Universit\`a della Svizzera italiana, Lugano, Switzerland). His work ranges from domain decomposition methods to the development of software libraries for large-scale scientific computing. He has created several open-source libraries (e.g., utopia, par_moonolith, ...) and contributed to open-source projects (e.g., MFEM, LLNL). In particular, he developed and implemented 
parallel methods for the variational transfer of discrete fields in support of multiphysics applications and contact problems;
Nonconforming discretization methods for flow in fractured porous media and fluid-structure interaction;
 algorithms and software for solving constrained nonlinear systems of equations.