Francesco Costanzo, Ph.D.
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Center for Neural Engineering
W-315 Millenium Science Complex
The Pennsylvania State University
University Park, PA 16802
Phone: 1-814-863-2030
Fax: 1-814-865-9974
Email: fmcostanzo@psu.edu
Rank: Full Professor
Years of Full-Time Faculty Service: 23
Professor Costanzo’s research in computational mechanics has focused on the development of computational tools rooted in the physics of the problems. The following publications highlight his most recent major accomplishments in research.
Method of Manufactured Solutions - 1
Magnitude of fluid velocity in a static evolution with stabilization.
Method of Manufactured Solutions - 2
Magnitude of fluid velocity in a dynamic evolution without stabilization.
Method of Manufactured Solutions - 3
Convergence rates for the L2-norm of the error at t = 0.02s for a dynamic evolution without stabilization.
A central problem in brain physiology is the transport of metabolites produced by cell func- tions in brain tissue from their production site to the main cerebrospinal fluid compartment. The modeling of these transport phenomena has traditionally focused on Fickian di usion within the extracellular space. More recent studies point to the existence of pathways for metabolite exchange with significant convective transport. Furthermore, evidence indicates that such convective component is driven by the pulsatile motion of arterial walls along the various elements of the brain vascular tree. These hypotheses need to be tested both against basic physiological and metabolical processes that rely on transport in brain parenchyma. They must also be tested against the mechanics of both di fusion and convection. This paper is the first rigorous result in the formulation of a stable and accurate numerical framework that can sort out the relative importance of the convective and di usive contributions to transport in brain by resolving the individual velocity fields of the interstitial fluid, vs. that of the surrounding tissue, vs. that of possible specific ionic species or neurotransmitters that one might be interested in tracking. This paper is foundational and future work will focus on testing adding di usive transport and considering physiological relevant scenarios to be com- pared with experiments. The National Science Foundation recently recommended for funding a project with F. Costanzo as the PI to complete the task in question.
Source:
Costanzo F. and S. T. Miller (2017), “An Arbitrary Lagrangian–Eulerian Finite Element Formulation for a Poroelasticity Problem Stemming from Mixture Theory”, Computer Methods in Applied Mechanics and Engineering, 323, pp. 64–97, DOI: 10.1016/j.cma.2017.05.006.
The propagation of acoustic waves in fluids is the basis for a plethora of lab-on-a-chip applica- tions, with the consequent prospect of revolutionizing point-of-care diagnostics in biomedical applications. While there have been many recent reports on the physics in confined reso- nant chamber, the physical understanding of acoustically-driven fluid and particle motion in confined leaky systems is limited. Not only is there a strong need for a mathematical and numerical framework in support of the devices in question, but there is also a need for the identification of “canonical” or benchmark experiments that can be used to validate the the- oretical framework. This paper lays the foundation for the analysis of microacoustofluidics by switching the framing of the problem from its traditional Eulerian view to an arbitrary Lagrangian-Eulerian formulation. This may seem a simple reformulation without modification of the underlying physics and therefore an exercise without much practical merit. However, this is not the case. Theoretical microacoustofluidics is, at its core, a homogenization prob- lems in time. Specifically, it consists in identifying dominant space and time scales and then using asymptotic expansions to create a cascade of boundary-value problems whose orders are defined by the separation of the identified scales. When used in practice, these expansions are truncated so as to consist of only on a finite number of problems. Therefore, the prob- lems generated by di erence kinematic frameworks yields di erent problems. In this paper we argue for the first time that an ALE perspective allows one to provide transparency to the boundary conditions used, the latter being only approximate in Eulerian formulations. In addition, the ALE formulation yields governing equations for the slow streaming that have less stringent regularity requirements compared to those yielded by the Eulerian framework. In very recent work, we have already provided practical results that demonstrated that the ALE formulation of the problems yields qualitative and quantitative results that are much closer to experimental results, so much so that the identification of an experimental bench- mark problem seems now within reach. Furthermore, we have demonstrated improved orders of convergence of the correspondent numerical implementation.† Continuation of this work in ongoing and corresponding publications are under review and in preparation.
Source:
Nama, N., T. J. Huang, and F. Costanzo (2017), “Acoustic Streaming: A Lagrangian– Eulerian Perspective”, Journal of Fluid Mechanics, 825, pp. 600–630,
DOI: 10.1017/jfm.2017.338.
Links to Videos:
https://youtu.be/cKmDjagN77k
Fig. 1
Microfluidic channel in a soft polymer actuated by surface acoustic waves. The surface acoustic waves leak energy into the polymer and microchannel and as a consequence, a pseudo-standing wave field arises. This field leads to acoustic streaming drag forces and radiation forces on suspended microparticles.
Fig. 2
ALE Formulation: magnitude of the Lagrangian-mean velocity (a) and of the Eulerian velocity (b) for a device with dimensions comparable to the acoustic wavelength. The bottom wall is actuated. The lines represent the streamlines of the respective velocities. The Lagrangian velocity streamlines do not cross the channel walls, indicating no mass flow across the channel walls, while the Eulerian velocity streamlines cross the channel walls as though there were an outflow across the channel walls.
Fig. 3
Ezb Formulation: magnitude of the (a) Lagrangian velocity and (b) Eulerian velocity for a device with dimensions comparable to the acoustic wavelength. The bottom wall is actuated. The Ezbc formulation (results in this figure) yields results that we believe are erroneous. The lines represent the streamlines of the respective velocities. Here the Lagrangian velocity streamlines cross the channel walls, indicating an unphysical mass flow across the channel walls. By contrast, consistent with the boundary conditions imposed in Ezbc formulation, here the Eulerian velocity streamlines do not cross the channel. These results are not supported by experimental evidence reported in Barnkob et al. (2016).
Fig. 1
Configuration of 3D benchmark. The results of the simulation consists in tracking the displacement of the point A(t) in the figure and in determining the hydrodynamic forces acting on rigid obstacle and flexible bar system.
Fig. 2
Vertical channel containing viscous fluid through which a small incompressible disk is descending: (a) system’s geometry; (b) initial conditions (disk released from rest in a quiescent fluid); (c) detail of mesh of the immersed body. The disk’s terminal velocity is denoted by Ut.
Fig. 3
Frame from animation showing the motion of a flexible flag as described in the FSI 2 benchmark by Hron and Turek.
FSI problems are very challenging to solve numerically and there are not closed-form solutions that can be generated (say, with the method of manufactured solutions) for the purpose of assessing convergence and computational efficiency. In lieu of closed-formed solutions, the FSI community has de facto agreed to use as benchmarks a collection of numerical tests compiled by Tureck and Hron in 2006. The significance of the above work is that, until now, no immersed method was ever been shown to strictly conform to the Tureck-Hron benchmarks. Costanzo’s group is the first to have produced results conforming to these benchmarks with an immersed method. This accomplishment is extraordinarily important in the FSI community.
Source:
Roy, S., L. Heltai, and F. Costanzo (2015), “Benchmarking the Immersed Finite Element Method for Fluid-Structure Interaction Problems”, Computers and Mathematics with Applications, 69(10), pp. 1167–1188. DOI: 10.1016/j.camwa.2015.03.012.
Links to Videos:
https://youtu.be/qt1DeCFZECQ
https://youtu.be/E6OyE3TSrVU
https://youtu.be/taQKI5KpRnw
Francesco Costanzo, Ph.D.
Center for Neural Engineering
W-315 Millenium Science Complex
The Pennsylvania State University
University Park, PA 16802
Phone: 1-814-863-2030
Fax: 1-814-865-9974
Email: fmcostanzo@psu.edu
