Davide Forti

A Rescaled Localized Radial Basis Function Interpolation On Non-Cartesian And Nonconforming Grids

In this paper we propose a rescaled localized radial basis function (RL-RBF) interpolation method, based on the use of compactly supported radial basis functions. Starting from the classical RBF interpolation technique, we introduce a rescaling that allows for exact interpolation of constant fields between nonconforming meshes without the use of an extra polynomial term. We also present two-dimensional and three-dimensional numerical examples on arbitrary finite element meshes to show that the RL-RBF interpolation leads to accurate results, fast evaluation, and easy parallelization of the algorithm. All the computations are carried out using the open source finite element library LifeV.

Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid–structure interaction coupling problems

We present some recent advances and improvements in shape parametrisation techniques of interfaces for reduced-order modelling with special attention to fluid–structure interaction problems and the management of structural deformations, namely, to represent them into a low-dimensional space (by control points). This allows to reduce the computational effort, and to significantly simplify the (geometrical) deformation procedure, leading to more efficient and fast reduced-order modelling applications in this kind of problems. We propose an efficient methodology to select the geometrical control points for the radial basis functions based on a modal greedy algorithm to improve the computational efficiency in view of more complex fluid–structure applications in several fields. The examples provided deal with aeronautics and wind engineering.

FaCSI: A block parallel preconditioner for fluid-structure interaction in hemodynamics

Modeling Fluid-Structure Interaction (FSI) in the vascular system is mandatory to reliably compute mechanical indicators in vessels undergoing large deformations. In order to cope with the computational complexity of the coupled 3D FSI problem after discretizations in space and time, a parallel solution is often mandatory. In this paper we propose a new block parallel preconditioner for the coupled linearized FSI system obtained after space and time discretization. We name it FaCSI to indicate that it exploits the Factorized form of the linearized FSI matrix, the use of static Condensation to formally eliminate the interface degrees of freedom of the fluid equations, and the use of a SIMPLE preconditioner for saddle-point problems. FaCSI is built upon a block Gauss-Seidel factorization of the FSI Jacobian matrix and it uses ad-hoc preconditioners for each physical component of the coupled problem, namely the fluid, the structure and the geometry. In the fluid subproblem, after operating static condensation of the interface fluid variables, we use a SIMPLE preconditioner on the reduced fluid matrix. Moreover, to efficiently deal with a large number of processes, FaCSI exploits efficient single field preconditioners, e.g., based on domain decomposition or the multigrid method. We measure the parallel performances of FaCSI on a benchmark cylindrical geometry and on a problem of physiological interest, namely the blood flow through a patient-specific femoropopliteal bypass. We analyze the dependence of the number of linear solver iterations on the cores count (scalability of the preconditioner) and on the mesh size (optimality)

Numerical modeling of fluid-structure interaction in arteries with anisotropic polyconvex hyperelastic and anisotropic viscoelastic material models at finite strains.

The accurate prediction of transmural stresses in arterial walls requires on the one hand robust and efficient numerical schemes for the solution of boundary value problems including fluid-structure interactions and on the other hand the use of a material model for the vessel wall that is able to capture the relevant features of the material behavior. One of the main contributions of this paper is the application of a highly nonlinear, polyconvex anisotropic structural model for the solid in the context of fluid-structure interaction, together with a suitable discretization. Additionally, the influence of viscoelasticity is investigated. The fluid-structure interaction problem is solved using a monolithic approach; that is, the nonlinear system is solved (after time and space discretizations) as a whole without splitting among its components. The linearized block systems are solved iteratively using parallel domain decomposition preconditioners. A simple - but nonsymmetric - curved geometry is proposed that is demonstrated to be suitable as a benchmark testbed for fluid-structure interaction simulations in biomechanics where nonlinear structural models are used. Based on the curved benchmark geometry, the influence of different material models, spatial discretizations, and meshes of varying refinement is investigated. It turns out that often-used standard displacement elements with linear shape functions are not sufficient to provide good approximations of the arterial wall stresses, whereas for standard displacement elements or F-bar formulations with quadratic shape functions, suitable results are obtained. For the time discretization, a second-order backward differentiation formula scheme is used. It is shown that the curved geometry enables the analysis of non-rotationally symmetric distributions of the mechanical fields. For instance, the maximal shear stresses in the fluid-structure interface are found to be higher in the inner curve that corresponds to clinical observations indicating a high plaque nucleation probability at such locations. Copyright

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).

A Fluid–Structure Interaction Algorithm Using Radial Basis Function Interpolation Between Non-Conforming Interfaces

We consider a fluid–structure interaction (FSI) problem discretized by finite elements featuring two different grids that do not necessarily agree on the interface separating the computational domain of the fluid from the one of the structure. After identifying a master domain (the structural domain) and a slave domain (the fluid domain), we build up two radial basis function (RBF) inter-grid operators, one Π fs from master to slave, and the other Π sf from slave to master. Then, we enforce the kinematic condition by equating the fluid velocity at the interface as the image through Π fs of the temporal derivative of the structural displacement. On the other hand, the dynamic interface condition is fulfilled via a variational method where the strong form of the structural normal stress is obtained as the image through Π sf of the strong form of the fluid normal stress. A numerical verification is carried out for a straight cylinder and for a patient-specific arterial bypass geometry. This new method is easy to implement and optimally accurate.

A Patient-Specific Computational Fluid Dynamics Model of the Left Atrium in Atrial Fibrillation: Development and Initial Evaluation

Atrial fibrillation (AF) is associated to a five-fold increase in the risk of stroke and AF strokes are especially severe. Stroke risk is connected to several AF related morphological and functional remodeling mechanisms which favor blood stasis and clot formation inside the left atrium. The goal of this study was therefore to develop a patient-specific computational fluid dynamics model of the left atrium which could quantify the hemodynamic implications of atrial fibrillation on a patient-specific basis. Hereto, dynamic patient-specific CT imaging was used to derive the 3D anatomical model of the left atrium by applying a specifically designed image segmentation algorithm. The computational model consisted in a fluid governed by the incompressible Navier-Stokes equations written in the Arbitrary Lagrangian Eulerian (ALE) frame of reference. In this paper, we present the developed model as well as its application to two AF patients. These initial results confirmed that morphological and functional remodeling processes associated to AF effectively reduce blood washout in the left atrium, thereby increasing the risk of clot formation. Our analysis is a step forward towards improved patient-specific stroke risk stratification and therapy planning.

Fluid-structure interaction for vascular flows: From supercomputers to laptops

There exists several models for the simulation of vascular flows; they span from simple circuit models, to full three dimensional ones which take into account detailed features of the blood and of the arterial wall. Each model comes with benefits and drawbacks, the main denominator being a compromise between detailed resolution requirements versus computational time. We first present a fluid-structure interaction computational model where both the fluid and the structure are three dimensional; in particular, the fluid includes modeling of large eddies by the variational multiscale method. After time and space discretisations carried out by finite differences and finite elements, respectively, we set up a parallel solver based on domain decomposition and a FaCSI preconditioner. These simulations allows to capture details of the flow dynamics and of the structure deformation even in the transitional regime characterizing the hemodynamics in the aorta. To complete a simulation of one heartbeat with 35 millions of degrees of freedom on 2048 cores it takes roughly 10 hours. We then reduce both the model and its numerical complexity. The structural model is simplified to a two dimensional membrane located at the fluid-structure interface and the fluid computational domain is fixed. For a fixed geometry and mesh, these assumptions allow to apply proper orthogonal decomposition and generate a space discretisation which has only few dozen degrees of freedom. It is then possible to perform the simulation of one heart-beat on a laptop in less than one second. The modeling and numerical reductions allows therefore a dramatic reduction of the computational time. However, the price to pay comes, on the one hand, in terms of the preparation of a reduced basis specific to the patient and the geometry of the vessel and, on the other hand, with a detriment of certain quantities of interest. For example, when using a finite element discretization with 9 millions of degrees of freedom, the offline part takes about 12 hours on 720 cores for the example provided in this work; in this case, the flow profiles in the aorta are pretty close to the full three dimensional model, but the wall shear stress is overestimated (although it follows the same temporal patterns).