M.D. de Tullio

An immersed boundary method for compressible flows using local grid refinement

This paper combines a state-of-the-art method for solving the three-dimensional preconditioned Navier-Stokes equations for compressible flows with an immersed boundary approach, to provide a Cartesian-grid method for computing complex flows over a wide range of the Mach number. Moreover, a flexible local grid refinement technique is employed to achieve high resolution near the immersed body and in other high-flow-gradient regions at a fraction of the cost required by a uniformly fine grid. The method is validated versus well documented steady and unsteady test problems, for a wide range of both Reynolds and Mach numbers. Finally, and most importantly, for the case of the laminar compressible steady flow past an NACA-0012 airfoil, a thorough mesh-refinement study shows that the method is second-order accurate.

Direct numerical simulation of the pulsatile flow through an aortic bileaflet mechanical heart valve

This work focuses on the direct numerical simulation of the pulsatile flow through a bileaflet mechanical heart valve under physiological conditions and in a realistic aortic root geometry. The motion of the valve leaflets has been computed from the forces exerted by the fluid on the structure both being considered as a single dynamical system. To this purpose the immersed boundary method, combined with a fluid–structure interaction algorithm, has shown to be an inexpensive and accurate technique for such complex flows. Several complete flow cycles have been simulated in order to collect enough phase-averaged statistics, and the results are in good agreement with experimental data obtained for a similar configuration. The flow analysis, strongly relying on the data accessibility provided by the numerical simulation, shows how some features of the leaflets motion depend on the flow dynamics and that the criteria for the red cell damages caused by the valve need to be formulated using very detailed analysis. In particular, it is shown that the standard Eulerian computation of the Reynolds stresses, usually employed to assess the risk of haemolysis, might not be adequate on several counts: (i) Reynolds stresses are only one part of the solicitation, the other part being the viscous stresses, (ii) the characteristic scales of the two solicitations are very different and the Reynolds stresses act on lengths much larger than the red cells diameter and (iii) the Eulerian zonal assessment of the stresses completely misses the information of time exposure to the solicitation which is a fundamental ingredient for the phenomenon of haemolysis. Accordingly, the trajectories of several fluid particles have been tracked in a Lagrangian way and the pointwise instantaneous viscous stress tensor has been computed along the paths. The tensor has been then reduced to an equivalent scalar using the von Mises criterion, and the blood damage index has been evaluated following Grigioni et al . ( Biomech. Model Mechanobiol ., vol. 4, 2005, p. 249).

A moving-least-squares immersed boundary method for simulating the fluid-structure interaction of elastic bodies with arbitrary thickness

A versatile numerical method is presented to predict the fluid-structure interaction of bodies with arbitrary thickness immersed in an incompressible fluid, with the aim of simulating different biological engineering applications. A direct-forcing immersed boundary method is adopted, based on a moving-least-squares approach to reconstruct the solution in the vicinity of the immersed surface. A simple spring-network model is considered for describing the dynamics of deformable structures, so as to easily model and simulate different biological systems that not always may be described by simple continuum models, without affecting the computational time and simplicity of the overall method. The fluid and structures are coupled in a strong way, in order to avoid instabilities related to large accelerations of the bodies. The effectiveness of the method is validated by means of several test cases involving: rigid bodies, either falling in a quiescent fluid, fluttering or tumbling, or transported by a shear flow; infinitely thin elastic structures with mass, such as a two-dimensional flexible filament and, concerning three-dimensional cases, a flapping flag and an inverted flag in a free stream; finally, a three-dimensional model of a bio-prosthetic aortic valve opening and closing under a pulsatile flowrate. A very good agreement is obtained in all the cases, comparing with available experimental data and numerical results obtained by different methods. In particular, the method is shown to be second-order accurate by means of a mesh-refinement study. Moreover, it is able to provide results comparable with those of sharp direct-forcing approaches, and can manage high pressure differences across the surface, still obtaining very smooth hydrodynamic forces.

Fluid–structure interaction of deformable aortic prostheses with a bileaflet mechanical valve

Two different aortic prostheses can be used for performing the Bentall procedure: a standard straight graft and the Valsalva graft that better reproduces the aortic root anatomy. The aim of the present work is to study the effect of the graft geometry on the blood flow when a bileaflet mechanical heart valve is used, as well as to evaluate the stress concentration near the suture line where the coronary arteries are connected to graft. An accurate three-dimensional numerical method is proposed, based on the immersed boundary technique. The method accounts for the interactions between the flow and the motion of the rigid leaflets and of the deformable aortic root, under physiological pulsatile conditions. The results show that the graft geometry only slightly influences the leaflets dynamics, while using the Valsalva graft the stress level near the coronary-root anastomoses is about half that obtained using the standard straight graft.

Evaluation of prosthetic-valved devices by means of numerical simulations

The in vivo evaluation of prosthetic device performance is often difficult, if not impossible. In particular, in order to deal with potential problems such as thrombosis, haemolysis, etc., which could arise when a patient undergoes heart valve replacement, a thorough understanding of the blood flow dynamics inside the devices interacting with natural or composite tissues is required. Numerical simulation, combining both computational fluid and structure dynamics, could provide detailed information on such complex problems. In this work, a numerical investigation of the mechanics of two composite aortic prostheses during a cardiac cycle is presented. The numerical tool presented is able to reproduce accurately the flow and structure dynamics of the prostheses. The analysis shows that the vortical structures forming inside the two different grafts do not influence the kinematics of a bileaflet valve or the main coronary flow, whereas major differences are present for the stress status near the suture line of the coronaries to the prostheses. The results are in agreement with in vitro and in vivo observations found in literature.

Recent Advances in the Development of an Immersed Boundary Method for Industrial Applications

This paper provides some recent developments of an immersed boundary method for solving flows of industrial interest at arbitrary Mach numbers. The method is based on the solution of the preconditioned compressible Favre-averaged Navier – Stokes equations closed by the k-ω low Reynolds number turbulence model. A flexible local grid refinement technique is implemented on parallel machines using a domain-decomposition approach and an edge-based data structure. Thanks to the efficient grid generation process, based on the ray-tracing technique, and the use of the METIS software, it is possible to obtain the partitioned grids to be assigned to each processor with a minimal effort by the user. This allows one to by-pass the very time consuming generation process of a body-fitted grid.

Optimal Perturbations in Boundary-Layer Flows Over Rough Surfaces

This work provides a three-dimensional energy optimization analysis, looking for perturbations inducing the largest energy growth at a finite time in a boundary-layer flow in the presence of roughness elements. The immersed boundary technique has been coupled with a Lagrangian optimization in a three-dimensional framework. Four roughness elements with different heights have been studied, inducing amplification mechanisms that bypass the asymptotical growth of Tollmien–Schlichting waves. The results show that even very small roughness elements, inducing only a weak deformation of the base flow, can strongly localize the optimal disturbance. Moreover, the highest value of the energy gain is obtained for a varicose perturbation. This result demonstrates the relevance of varicose instabilities for such a flow and shows a different behavior with respect to the secondary instability theory of boundary layer streaks.

An Immersed Boundary Method for Conjugate Heat Transfer Problems

This paper provides an immersed boundary method using a flexible local grid refinement technique for solving conjugate-heat-transfer problems. The proposed method is used to solve the flow past a heated hollow cylinder inside a channel together with the temperature field within the cylinder and then to predict turbomachinery blade cooling.© 2010 ASME

Immersed boundary technique for compressible flow simulations on semi-structured grids

The Immersed Boundary (IB) method simplifies the grid generation process for the simulation of flows with complex and/or moving solid boundaries by avoiding the need for a body-fitted mesh. The IB technique was originally developed for incompressible flows [1, 2, 3] using Cartesian grids. Recently, some of the authors have extended the IB technique to compressible flows [4] using the preconditioned Navier–Stokes equations, which allow one to provide accurate and efficient solutions for a wide range of the Mach number. To date, IB methods employ structured grids, which allow only limited control on the distribution of the grid points in the computational domain; in fact, clustering of grid points is needed close to solid boundaries in order to describe its geometry accurately and, since mesh lines run through the entire computational domain, a high concentration of grid points is obtained also in regions away from the solid walls, where flow gradients are usually small.

An Immersed-Boundary Method for 3D Compressible Viscous Flows

This paper combines a state-of-the-art method for solving the preconditioned compressible Navier{Stokes equations accurately and ecien tly for a wide range of the Mach number with an immersed-boundary approach which allows to use Cartesian grids for arbitrarily complex geometries. The method is validated versus well documented test problems for a wide range of the Reynolds and Mach numbers and has been employed to compute the o w past a cylinder oscillating in the cross-o w direction, showing its capability to easily and accurately handle moving geometries. The method has been also extended to threedimensional o ws and it has been validated versus subsonic and supersonic o ws past a sphere. The numerical results demonstrate the eciency and versatility of the proposed approach as well as its accuracy, from incompressible to supersonic o w conditions, for moderate values of the Reynolds number.