Gonçalo Pena

High-order fluid-structure interaction in 2D and 3D application to blood flow in arteries

This paper addresses the numerical approximation of fluid-structure interaction (FSI) problems through the arbitrary Lagrangian Eulerian (ALE) framework, high-order methods and a Dirichlet-Newmann approach for the coupling. The paper is divided into two main parts. The first part concerns the discretization method for the FSI problem. We introduce an improved ALE map, capable of handling curved geometries in 2D and 3D in a unified manner, that is based on a local differential operator. We also propose a minimal continuous interior penalty (CIP) stabilization term for the fluid discretization that accounts for a smaller computational effort, while stabilizing the flow regime. The second part is dedicated to validating our numerical strategy through a benchmark and some applications to blood flow in arteries.

Construction of a high order fluid-structure interaction solver

Accuracy is critical if we are to trust simulation predictions. In settings such as fluid-structure interaction, it is all the more important to obtain reliable results to understand, for example, the impact of pathologies on blood flows in the cardiovascular system. In this paper, we propose a computational strategy for simulating fluid structure interaction using high order methods in space and time. First, we present the mathematical and computational core framework, Life, underlying our multi-physics solvers. Life is a versatile library allowing for 1D, 2D and 3D partial differential solves using h/p type Galerkin methods. Then, we briefly describe the handling of high order geometry and the structure solver. Next we outline the high-order space-time approximation of the incompressible Navier-Stokes equations and comment on the algebraic system and the preconditioning strategy. Finally, we present the high-order Arbitrary Lagrangian Eulerian (ALE) framework in which we solve the fluid-structure interaction problem as well as some initial results.

Iontophoretic transdermal drug delivery: a multi-layered approach

We present a multi-layer mathematical model to describe the transdermal drug release from an iontophoretic system. The Nernst-Planck equation describes the basic convection-diffusion process, with the electric potential obtained by solving the Laplaces equation. These equations are complemented with suitable interface and boundary conditions in a multi-domain. The stability of the mathematical problem is discussed in different scenarios and a finite-difference method is used to solve the coupled system. Numerical experiments are included to illustrate the drug dynamics under different conditions.

Transdermal iontophoresis—A quantitative and qualitative study

Abstract The use of enhancers to increase the drug molecules penetration into target tissues is a usual technique in drug delivery. In transdermal drug delivery, electric fields are often used to increase the drug transport through the skin. In this paper we study a drug delivery mechanism from a reservoir which is in contact with the skin. We assume that the drug transport in the coupled system is enhanced by a small electric field that induces a convective field. We establish energy estimates for the coupled system and we propose a semi-analytical discrete coupled model that mimics the continuous model. The qualitative behaviour of the system is illustrated.

On the exponential decay of waves with memory

In this paper we consider general linear damped wave equations with memory. We establish energy estimates that under the assumption of exponentially bounded kernels, induce exponential decaying solutions. Numerical waves that mimic their continuous counterpart are also introduced using a finite element approach.