Vesicle dynamics in confined steady and harmonically modulated Poiseuille flows

We present a numerical study of the time-dependent motion of a two-dimensional vesicle in a channel under an imposed flow. In a Poiseuille flow the shape of the vesicle depends on the flow strength, the mechanical properties of the membrane, and the width of the channel as reported in the past. This study is focused on the centered snaking (CSn) shape, where the vesicle shows an oscillatory motion like a swimmer flagella even though the flow is stationary. We quantify this behavior by the amplitude and frequency of the oscillations of the vesicle's center of mass. We observe regions in parameter space, where the CSn coexists with the parachute or the unconfined slipper. The influence of an amplitude modulation of the imposed flow on the dynamics and shape of the snaking vesicle is also investigated. For large modulation amplitudes transitions to static shapes are observed. A smaller modulation amplitude induces a modulation in amplitude and frequency of the center of mass of the snaking vesicle. In a certain parameter range we find that the center of mass oscillates with a constant envelope indicating the presence of at least two stable states.Comment: 10 pages, 7 figure

A Computational Fluid-Structure Interaction Method for Simulating Supersonic Parachute Inflation

Following the successful landing of the Curiosity rover on the Martian surface in 2012, NASA/JPL conducted the low-density supersonic decelerator (LDSD) missions to develop large diameter parachutes to land the increasingly heavier payloads being sent to the Martian surface. Unexpectedly, both of the tested parachutes failed far below their design loads. It became clear that there was an inability to model and predict loads that occur during supersonic parachute inflation. In this dissertation, a new computational method that was developed to provide NASA with the capability to simulate supersonic parachute inflation is presented and validated. The method considers the loose coupling of two different immersed boundary methods with a nonlinear finite element solver. Following validation on canonical FSI problems, methods to simulate the permeability of parachute broadcloth and to identify and enforce contact in parallel are presented and validated. The coupled solvers are first applied to the supersonic parachute problem on a sub-scale MSL parachute and capsule geometry, and subsequently, a full-scale test flight from the Advanced Supersonic Parachute Inflation Research Experiments (ASPIRE) is simulated. To the best of the author’s knowledge, these are the first FSI simulations to match the ASPIRE flight test data

A partition of unity approach to fluid mechanics and fluid-structure interaction

For problems involving large deformations of thin structures, simulating fluid-structure interaction (FSI) remains challenging largely due to the need to balance computational feasibility, efficiency, and solution accuracy. Overlapping domain techniques have been introduced as a way to combine the fluid-solid mesh conformity, seen in moving-mesh methods, without the need for mesh smoothing or re-meshing, which is a core characteristic of fixed mesh approaches. In this work, we introduce a novel overlapping domain method based on a partition of unity approach. Unified function spaces are defined as a weighted sum of fields given on two overlapping meshes. The method is shown to achieve optimal convergence rates and to be stable for steady-state Stokes, Navier-Stokes, and ALE Navier-Stokes problems. Finally, we present results for FSI in the case of a 2D mock aortic valve simulation. These initial results point to the potential applicability of the method to a wide range of FSI applications, enabling boundary layer refinement and large deformations without the need for re-meshing or user-defined stabilization.Comment: 34 pages, 15 figur

Fully Eulerian models for the numerical simulation of capsules with an elastic bulk nucleus

In this paper, we present a computational framework based on fully Eulerian models for fluid-structure interaction for the numerical simulation of biological capsules. The flexibility of such models, given by the Eulerian treatment of the interface and deformations, allows us to easily deal with the large deformations experienced by the capsule. The modeling of the membrane is based on the full membrane elasticity model introduced in (Milcent, T., Maitre, E. (2016)) that is capable of capturing both area and shear variations thanks to the so-called backward characteristics. In the validation section several test cases are presented with the goal of comparing our results to others present in the literature. In this part, the comparisons are done with different well-known configurations (capsule in shear flow and square-section channel), and by deepening the effect of the elastic constitutive law and capillary number on the membrane dynamics. Finally, to show the potential of this framework we introduce a new test case that describes the relaxation of a capsule in an opening channel. In order to increase the challenges of this test we study the influence of an internal nucleus, modeled as a hyperelastic solid, on the membrane evolution. Several numerical simulations are presented to deeply study its influence by modifying the characteristic parameters of the nucleus (size and elastic parameter)