Efficient split-step schemes for fluid–structure interaction involving incompressible generalised Newtonian flows

Blood flow, dam or ship construction and numerous other problems in biomedical and general engineering involve incompressible flows interacting with elastic structures. Such interactions heavily influence the deformation and stress states which, in turn, affect the engineering design process. Therefore, any reliable model of such physical processes must consider the coupling of fluids and solids. However, complexity increases for non-Newtonian fluid models, as used, e.g., for blood or polymer flows. In these fluids, subtle differences in the local shear rate can have a drastic impact on the flow and hence on the coupled problem. There, existing (semi-) implicit solution strategies based on split-step or projection schemes for Newtonian fluids are not applicable, while extensions to non-Newtonian fluids can lead to substantial numerical overhead depending on the chosen fluid solver. To address these shortcomings, we present here a higher-order accurate, added-mass-stable fluid–structure interaction scheme centered around a split-step fluid solver. We compare several implicit and semi-implicit variants of the algorithm and verify convergence in space and time. Numerical examples show good performance in both benchmarks and an idealised setting of blood flow through an abdominal aortic aneurysm considering physiological parameters

A monolithic and a partitioned Reduced Basis Method for Fluid-Structure Interaction problems

The aim of this work is to present an overview about the combination of the Reduced Basis Method (RBM) with two different approaches for Fluid-Structure Interaction (FSI) problems, namely a monolithic and a partitioned approach. We provide the details of implementation of two reduction procedures, and we then apply them to the same test case of interest. We first implement a reduction technique that is based on a monolithic procedure where we solve the fluid and the solid problems all at once. We then present another reduction technique that is based on a partitioned (or segregated) procedure: the fluid and the solid problems are solved separately and then coupled using a fixed point strategy. The toy problem that we consider is based on the Turek-Hron benchmark test case, with a fluid Reynolds number Re = 100

Numerical approximation of cardiac electro-fluid-mechanical models:coupling strategies for large-scale simulation

The mathematical modeling of the heart involves several challenges, which are intrinsically related to the complexity of its function. A satisfactory cardiac model must be able to describe a wide range of different processes, such as the evolution of the transmembrane potential in the myocardium, the deformation caused by the muscles contraction, and the dynamics of the blood inside the heart chambers. In this work, we focus on the coupling of the electrophysiology, the active and the passive mechanics, and the fluid dynamics of the blood in the left ventricle (LV) of the human heart. The models describing the previously mentioned processes are called âsingle core modelsâ, and can be regarded as the building blocks of an âintegrated modelâ. In this thesis, we first review the isolated single core mathematical models for the description of the LV function, and discuss their space and time discretizations with particular emphasis on the coupling conditions. We consider both implicit and semi-implicit schemes for the time discretization. The fully discretized single core problems thus obtained are then combined to define integrated electromechanics and electrofluidmechanics problems. We then focus on the numerical coupling strategy for the electromechanics solver in the framework of the active strain formulation. First, we propose a monolithic strategy where the discretized core models are solved simultaneously; then, several novel segregated strategies, where the discretized core models are solved sequentially, are proposed and systematically compared with each other. The segregated strategies are obtained by exploiting a Godunov splitting scheme, which introduces a first order error on the solution. We show that, while the monolithic approach is more accurate and more stable for relatively large timesteps, segregated approaches allow to solve the integrated problem much more efficiently in terms of computational resources. Moreover, with segregated approaches, it is possible to use different timesteps for the different core models in a staggered fashion, thus further improving the computational efficiency of the schemes. The monolithic and the segregated strategies for the electromechanics are used to solve a benchmark problem with idealized geometry: the results are then compared in terms of accuracy and efficiency. We numerically confirm that the segregated strategies are accurate at least of order one. In light of the results obtained, we employ the proposed strategies to simulate the electromechanics of a subject-specific LV for a full heartbeat. We simulate both healthy and pathological scenarios: in the latter case, we account for an ischemic necrosis of the tissue and analyze several clinical indicators such as pressure-volume loops and the end systolic pressure-volume relationship. Finally, we use the proposed strategies to simulate the electrofluidmechanics of a realistic LV during the systolic phase of the heartbeat. When defining the integrated cardiac models, we establish a preprocess pipeline aimed at preparing geometries and data for both idealized and subject-specific simulations. The pipeline is succesfully used for the setting up of large scale simulations in a high performance computing framework, where the (strong and weak) scalability of the proposed coupling strategies is assessed

A Monolithic Approach to Fluid–Composite Structure Interaction

We study a nonlinear fluid–structure interaction (FSI) problem between an incompressible, viscous fluid and a composite elastic structure consisting of two layers: a thin layer (membrane) in direct contact with the fluid, and a thick layer (3D linearly elastic structure) sitting on top of the thin layer. The coupling between the fluid and structure, and the coupling between the two structures is achieved via the kinematic and dynamic coupling conditions modeling no-slip and balance of forces, respectively. The coupling is evaluated at the moving fluid–structure interface with mass, i.e., the thin structure. To solve this nonlinear moving-boundary problem in 3D, a monolithic, fully implicit method was developed, and combined with an arbitrary Lagrangian–Eulerian approach to deal with the motion of the fluid domain. This class of problems and its generalizations are important in e.g., modeling FSI between blood flow and arterial walls, which are known to be composed of several different layers, each with different mechanical characteristics and thickness. By using this model we show how multi-layered structure of arterial walls influences the pressure wave propagation in arterial walls, and how the presence of atheroma and the presence of a vascular device called stent, influence intramural strain distribution throughout different layers of the arterial wall. The detailed intramural strain distribution provided by this model can be used in conjunction with ultrasound B-mode scans as a predictive tool for an early detection of atherosclerosis (Zahnd et al. in IEEE international on ultrasonics symposium (IUS), pp 1770–1773, 2011)