IB2d : a Python and MATLAB implementation of the immersed boundary method

The development of fluid-structure interaction (FSI) software involves trade-offs between ease of use, generality, performance, and cost. Typically there are large learning curves when using low-level software to model the interaction of an elastic structure immersed in a uniform density fluid. Many existing codes are not publicly available, and the commercial software that exists usually requires expensive licenses and may not be as robust or allow the necessary flexibility that in house codes can provide. We present an open source immersed boundary software package, IB2d, with full implementations in both MATLAB and Python, that is capable of running a vast range of biomechanics models and is accessible to scientists who have experience in high-level programming environments. IB2d contains multiple options for constructing material properties of the fiber structure, as well as the advection-diffusion of a chemical gradient, muscle mechanics models, and artificial forcing to drive boundaries with a preferred motion

An IB Method for Non-Newtonian-Fluid Flexible-Structure Interactions in Three-Dimensions

Problems involving fluid flexible-structure interactions (FFSI) are ubiquitous in engineering and sciences. Peskin’s immersed boundary (IB) method is the first framework for modeling and simulation of such problems. This paper addresses a three-dimensional extension of the IB framework for non-Newtonian fluids which include power-law fluid, Oldroyd-B fluid, and FENE-P fluid. The motion of the non-Newtonian fluids are modelled by the lattice Boltzmann equations (D3Q19 model). The differential constitutive equations of Oldroyd-B and FENE-P fluids are solved by the D3Q7 model. Numerical results indicate that the new method is first-order accurate and conditionally stable. To show the capability of the new method, it is tested on three FFSI toy problems: a power-law fluid past a flexible sheet fixed at its midline, a flexible sheet being flapped periodically at its midline in an Oldroyd-B fluid, and a flexible sheet being rotated at one edge in a FENE-P fluid

Interactive 3D simulation for fluid–structure interactions using dual coupled GPUs

The scope of this work involves the integration of high-speed parallel computation with interactive, 3D visualization of the lattice-Boltzmann-based immersed boundary method for fluid–structure interaction. An NVIDIA Tesla K40c is used for the computations, while an NVIDIA Quadro K5000 is used for 3D vector field visualization. The simulation can be paused at any time step so that the vector field can be explored. The density and placement of streamlines and glyphs are adjustable by the user, while panning and zooming is controlled by the mouse. The simulation can then be resumed. Unlike most scientific applications in computational fluid dynamics where visualization is performed after the computations, our software allows for real-time visualizations of the flow fields while the computations take place. To the best of our knowledge, such a tool on GPUs for FSI does not exist. Our software can facilitate debugging, enable observation of detailed local fields of flow and deformation while computing, and expedite identification of ‘correct’ parameter combinations in parametric studies for new phenomenon. Therefore, our software is expected to shorten the ‘time to solution’ process and expedite the scientific discoveries via scientific computing

Immersed boundary simulations and tools for studying insect flight and other applications

All organisms must deal with fluid transport and interaction, whether it be internal, such as lungs moving air for the extraction of oxygen, or external, such as the expansion and contraction of a jellyfish bell for locomotion. Most organisms are highly deformable and their elastic deformations can be used to move fluid, move through fluid, and resist fluid forces. A particularly effective numerical method for biological fluid-structure interaction simulations is the immersed boundary (IB) method. An important feature of this method is that the fluid is discretized separately from the boundary interface, meaning that the two meshes do not need to conform with each other. This thesis covers the development of a new software tool for the semi-automated creation of finite difference meshes of complex 2D geometries for use with immersed boundary solvers IB2d and IBAMR, alongside two examples of locomotion - the flight of tiny insects and the metachronal paddling of brine shrimp. As mentioned, an advantage of the IB method is that complex geometries, e.g., internal or external morphology, can easily be handled without the need to generate matching grids for both the fluid and the structure. Consequently, the difficulty of modeling the structure lies often in discretizing the boundary of the complex geometry (morphology). Both commercial and open source mesh generators for finite element methods have long been established; however, the traditional immersed boundary method is based on a finite difference discretization of the structure. In chapter \ref{chap:meshmerizeme}, I present a software library called MeshmerizeMe for obtaining finite difference discretizations of boundaries for direct use in the 2D immersed boundary method. This library provides tools for extracting such boundaries as discrete mesh points from digital images. Several examples of how the method can be applied are given to demonstrate the effectiveness of the software, including passing flow through the veins of insect wings, within lymphatic capillaries, and around starfish using open-source immersed boundary software. As an example of insect flight, I present a 3D model of clap and fling. Of the smallest insects filmed in flight, most if not all clap their wings together at the end of the upstroke and fling them apart at the beginning of the downstroke. This motion increases the strength of the leading edge vortices generated during the downstroke and augments the lift. At the Reynolds numbers ($Re$) relevant to flight in these insects (roughly $4<Re<40$), the drag produced during the fling is substantial, although this can be reduced through the presence of wing bristles, chordwise wing flexibility, and more complex wingbeat kinematics. It is not clear how flexibility in the spanwise direction of the wings can alter the lift and drag generated. In chapter \ref{chap:clapfling}, a hybrid version of the immersed boundary method with finite elements is used to simulate a 3D idealized clap and fling motion across a range of wing flexibilities. I find that spanwise flexibility, in addition to three-dimensional spanwise flow, can reduce the drag forces produced during the fling while maintaining lift, especially at lower $Re$. While the drag required to fling 2D wings apart may be more than an order of magnitude higher than the force required to translate the wings, this effect is significantly reduced in 3D. Similar to previous studies, dimensionless drag increases dramatically for $Re<20$, and only moderate increases in lift are observed. Both lift and drag decrease with increasing wing flexibility, but below some threshold, lift decreases much faster. This study highlights the importance of flexibility in both the chordwise and spanwise directions for low $Re$ insect flight. The results also suggest that there is a large aerodynamic cost if insect wings are too flexible. My second application of locomotion pertains to a 2D model of swimming, specifically the method known as metachronal paddling. This method is used by a variety of organisms to propel themselves through a fluid. This mode of swimming is characterized by an array of appendages that beat out of phase, such as the swimmerets used by long-tailed crustaceans like crayfish and lobster. This form of locomotion is typically observed over a range of Reynolds numbers greater than 1 where the flow is dominated by inertia. The majority of experimental, modeling, and numerical work on metachronal paddling has been conducted on the higher Reynolds number regime (order 100). In this chapter, a simplified numerical model of one of the smaller metachronal swimmers, the brine shrimp, is constructed. Brine shrimp are particularly interesting since they swim at Reynolds numbers on the order of 10 and sprout additional paddling appendages as they grow. The immersed boundary method is used to numerically solve the fluid-structure interaction problem of multiple rigid paddles undergoing cycles of power and return strokes with a constant phase difference and spacing that are based on brine shrimp parameters. Using a phase difference of 8\%, the volumetric flux and efficiency per paddle as a function of the Reynolds number and the spacing between legs is quantified. I find that the time to reach periodic steady state for adult brine shrimp is large ($\approx 150$ stroke cycles) and decreases with decreasing Reynolds number. Both efficiency and average flux increase with Reynolds number. In terms of leg spacing, the average flux decreases with increased spacing while the efficiency is maximized for intermediate leg spacing.Doctor of Philosoph

The Fluid Dynamics of Heart Development: The effect of morphology on flow at several stages

Proper cardiogenesis requires a delicate balance between genetic and environmental (epigenetic) signals, and mechanical forces. While many cellular biologists and geneticists have extensively studied heart morphogenesis using various experimental techniques, only a few scientists have begun using mathematical modeling as a tool for studying cardiogenic events. Hemodynamic processes, such as vortex formation, are important in the generation of shear at the endothelial surface layer and strains at the epithelial layer, which aid in proper morphology and functionality. The purpose of this thesis is to study the underlying fluid dynamics in various stages on heart development, in particular, the morphogenic stages when the heart is a linear heart tube as well as during the onset of ventricular trabeculation. Previous mathematical models of the linear heart tube stage have focused on mechanisms of valveless pumping, whether dynamic suction pumping (impedance pumping) or peristalsis; however, they all have neglected hematocrit. The impact of blood cells was examined by fluid-structure interaction simulations, via the immersed boundary method. Moreover, electrophysiology models were incorporated into an immersed boundary framework, and bifurcations within the morphospace were studied that give rise to a spectrum of pumping regimes, with peristaltic-like waves of contraction and impedance pumping at the extremes. Lastly, effects of resonant pumping, damping, and boundary inertial effects (added mass) were studied for dynamic suction pumping. The other stage of heart development considered here is during the onset of ventricular trabeculation. This occurs after the heart has undergone the cardiac looping stage and now is a multi-chambered pumping system with primitive endocardial cushions, which act as precursors to valve leaflets. Trabeculation introduces complex morphology onto the inner lining of the endocardium in the ventricle. This transition of a smooth endocardium to one with complex geometry, may have significant effect on the intracardial fluid dynamics and stress distribution within emrbyonic hearts. Previous studies have not included these geometric perturbations along the ventricular endocardium. The role of trabeculae on intracardial (and intertrabecular) flows was studied using two different mathematical models implemented within an immersed boundary framework. It is shown that the trabecular geometry and number density have a significant effect on such flows. Furthermore this thesis also focused attention to the creation of software for scientists and engineers to perform fluid-structure interaction simulations at an accelerated rate, in user-friendly environments for beginner programmers, e.g., MATLAB or Python 3.5. The software, IB2d, performs fully coupled fluid-structure interaction problems using Charles Peskin's immersed boundary method. IB2d is capable of running a vast range of biomechanics models and contains multiple options for constructing material properties of the fiber structure, advection-diffusion of a chemical gradient, muscle mechanics models, Boussinesq approximations, and artificial forcing to drive boundaries with a preferred motion. The software currently contains over 50 examples, ranging from rubber-bands oscillating to flow past a cylinder to a simple aneurysm model to falling spheres in a chemical gradient to jellyfish locomotion to a heart tube pumping coupled with electrophysiology, muscle, and calcium dynamics modelsDoctor of Philosoph