Fluid-structure interaction simulation of prosthetic aortic valves : comparison between immersed boundary and arbitrary Lagrangian-Eulerian techniques for the mesh representation

In recent years the role of FSI (fluid-structure interaction) simulations in the analysis of the fluid-mechanics of heart valves is becoming more and more important, being able to capture the interaction between the blood and both the surrounding biological tissues and the valve itself. When setting up an FSI simulation, several choices have to be made to select the most suitable approach for the case of interest: in particular, to simulate flexible leaflet cardiac valves, the type of discretization of the fluid domain is crucial, which can be described with an ALE (Arbitrary Lagrangian-Eulerian) or an Eulerian formulation. The majority of the reported 3D heart valve FSI simulations are performed with the Eulerian formulation, allowing for large deformations of the domains without compromising the quality of the fluid grid. Nevertheless, it is known that the ALE-FSI approach guarantees more accurate results at the interface between the solid and the fluid. The goal of this paper is to describe the same aortic valve model in the two cases, comparing the performances of an ALE-based FSI solution and an Eulerian-based FSI approach. After a first simplified 2D case, the aortic geometry was considered in a full 3D set-up. The model was kept as similar as possible in the two settings, to better compare the simulations' outcomes. Although for the 2D case the differences were unsubstantial, in our experience the performance of a full 3D ALE-FSI simulation was significantly limited by the technical problems and requirements inherent to the ALE formulation, mainly related to the mesh motion and deformation of the fluid domain. As a secondary outcome of this work, it is important to point out that the choice of the solver also influenced the reliability of the final results

Numerical Simulations of Flow around Copepods: Challenges and Future Directions

Copepods are small aquatic creatures which are abundant in oceans as a major food source for fish, thereby playing a vital role in marine ecology. Because of their role in the food chain, copepods have been subject to intense research through different perspectives from anatomy, form-function biology, to ecology. Numerical simulations can uniquely support such investigations by quantifying: (i) the force and flow generated by different parts of the body, thereby clarify the form-function relation of each part; (ii) the relation between the small-scale flow around animal and the large-scale (e.g., oceanic) flow of its surroundings; and (iii) the flow and its energetics, thereby answering ecological questions, particularly, the three major survival tasks, i.e., feeding, predator avoidance, and mate-finding. Nevertheless, such numerical simulations need to overcome challenges involving complex anatomic shape of copepods, multiple moving appendages, resolving different scales (appendage-, animal- to large-scale). The numerical methods capable of handling such problems and some recent simulations are reviewed. At the end, future developments necessary to simulate copepods from animal- to surrounding-scale are discussed

Why don't mackerels swim like eels? The role of form and kinematics on the hydrodynamics of undulatory swimming

video entry for gallery of fluid motion 2008We carry out numerical simulations with 3D self-propelled virtual swimmers, a mackerel (M) and an eel (E), to elucidate the role of form (body shape) and kinematics carangiform (C) vs. anguilliform (A) on the hydrodynamics of undulatory swimming. The motion of the fish mean line is prescribed but the forward swimming speed is calculated via the fluid-structure interaction (FSI) numerical approach of Borazjani et al [J. Comp. Physics, 227(16), 2008]. We consider: 1) a mackerel swimming as mackerel do in nature (M-C); 2) a mackerel swimming with anguilliform kinematics (M-A); 3) an eel swimming as eels do (E-A); and 4) an eel swimming with carangiform kinematics (E-C). Virtual swimmers with the same body shape race each other with different kinematics (M-C vs. M-A and E-C vs. E-A) in the same fluid (fixed viscosity) and with the same tail beat frequency. Regardless of body shape, anguilliform kinematics win the race in the transitional regime (Re = 4000) while carangiform kinematics prevail in the inertial regime (Inviscid limit). Our results support the notion that hydrodynamic considerations have played a role in the evolution of fish shapes and kinematics since in nature anguilliform kinematics are preferred in the transitional regime while carangiform kinematics are preferred in the inertial regime. Out results also show that the 3D structure of fish wakes (single vs. double row vortices) is largely independent of body shape and kinematics and support our previous findings [J. Exp. Biol. 211(10) 2008] that the Strouhal number is the key governing parameter.This work was supported by NSF Grants 0625976 and EAR-0120914, and the Minnesota Supercomputing Institute

A kinematics-based model for the settling of gravity-driven arbitrary-shaped particles on a surface.

A discrete model is proposed for settling of an arbitrary-shaped particle onto a flat surface under the gravitational field. In this method, the particle dynamics is calculated such that (a) the particle does not create an overlap with the wall and (b) reaches a realistic equilibrium state, which are not guaranteed in the conventional discrete element methods that add a repulsive force (torque) based on the amount of overlap between the particle and the wall. Instead, upon the detection of collision, the particle's kinematics is modified depending on the type of contact, i.e., point, line, and surface types, by assuming the contact point/line as the instantaneous center/line of rotation for calculating the rigid body dynamics. Two different stability conditions are implemented by comparing the location of the projection of the center of mass on the wall along gravity direction against the contact points to identify the equilibrium (stable) state on the wall for particles with multiple contact points. A variety of simulations are presented, including smooth surface particles (ellipsoids), regular particles with sharp edges (cylinders and pyramids) and irregular-shaped particles, to show that the method can provide the analytically-known equilibrium state