Fluid Dynamics

Blood flow in medium and large arteries are described by the incompressible Navier-Stokes equations.

The research focused on efficient solvers and preconditioners for the saddle-point problem arising from the finite element approximation of the NS equations. In particular inexact block LU factorization preconditioners have been studied.

Another topic concerns the well-posedness and stability of the fluid problem in a moving domain.

Other research fields includes reduced models and geometrical parametrization, and including uncertainty quantification and sensitivity analysis.

In view of clinical pathological applications (stenotic carotids) the research at MOX laboratory focuses also on turbulence phenomena, in particular with the Large Eddy Simulation strategy.

A parallel research field concerns advection of solutes in blood flow, such as oxygen transport and drug release from medical stents.

Publications:

  1. P. Gervasio, F. Saleri, Stabilized Spectral Element Approximation for the Navier Stokes Equations, Numerical Methods for Partial Differential Equations, 14(1), pp. 115-41, 1998
  2. L. Formaggia and F. Nobile, A stability analysis for the arbitrary Lagrangian Eulerian formulation with finite elements, East-West J. Numer. Math., 7(2), pp.105–132, 1999
  3. A. Quarteroni, F.Saleri, A. Veneziani, Analysis of the Yosida Method for the Incompressible Navier-Stokes Equations, Journal de Mathématiques Pures et Appliquées, 78(5), pp. 473-503, 1999
  4. A. Quarteroni, F. Saleri, A. Veneziani, Factorization methods for the Time advancing of the incompressible Navier-Stokes equations, Computer Methods in Applied Mechanics and Engineering, 188(1-3), pp. 505-26, 2000
  5. A. Quarteroni, A. Veneziani, P. Zunino, Mathematical and numerical modeling of solute dynamics in blood flow and arterial walls, SIAM Journal on Numerical Analysis, 39(5), pp. 1488-511, 2001
  6. A. Quarteroni, A. Veneziani, P. Zunino, A domain decomposition method for advection-diffusion processes with application to blood solutes, SIAM Journal on Scientific Computing, 23(6), pp. 1959-80, 2002
  7. A. Veneziani, Block factorized preconditioners for high-order accurate in time approximation of the Navier-Stokes equations, Numerical Methods For Partial Differential Equations, 19, pp. 487-510, 2003
  8. A. Quarteroni, G. Rozza, Optimal control and shape optimization of aorto-coronaric bypass anastomoses, Mathematical Models and Methods in Applied Sciences, 13(12), pp. 1801-1823, 2003
  9. L. Formaggia and F. Nobile, Stability analysis of second order time accurate schemes for ALE-FEM, Comp. Meth. Appl. Mech. Engrg., 193, pp.4097–4116, 2004
  10. P. Zunino, Multidimensional pharmacokinetic models applied to the design of drug-eluting stents, Cardiovascular Engineering, 4(2), pp. 181-191, 2004
  11. A. Gauthier, F. Saleri, A. Veneziani, A fast preconditioner for the incompressible Navier-Stokes equations, Computing and Visualization in Science, 6, pp. 105-12, 2004
  12. M. Prosi, P. Zunino, K. Perktold, A. Quarteroni, Mathematical and numerical models for transfer of low-density lipoproteins through the arterial walls: A new methodology for the model set up with applications to the study of disturbed lumenal flow, Journal of Biomechanics, 38(4), pp. 903-917, 2005
  13. F. Saleri, A. Veneziani, Pressure correction algebraic-splitting methods for the incompressible Navier-Stokes equations, SIAM Journal on Numerical Analysis, 43(1), pp.174-94, 2005
  14. P. Gervasio, F. Saleri, Algebraic fractional-step schemes for time-dependent incompressible Navier-Stokes equations, Journal of Scientific Computing, 27(1-3), pp.257-69, 2006
  15. P. Gervasio, F. Saleri, A. Veneziani, Algebraic splitting methods methods for the incompressible Navier-Stokes equations, Journal of Computational Physics, 214, pp. 347-65, 2006
  16. R. Ponzini, C. Vergara, A. Redaelli, A. Veneziani, Reliable CFD-based estimation of flow rate in haemodynamics measures, Ultrasound in Medicine & Biology, 32(10), pp. 1545-55, 2006
  17. V. Agoshkov, A. Quarteroni, G. Rozza, A mathematical approach in the design of arterial bypass using unsteady Stokes equations, Journal of Scientific Computing, 28(2-3), pp. 139-165, 2006
  18. V. Agoshkov, A. Quarteroni, G. Rozza, Shape design in aorto-coronaric bypass anastomoses using perturbation theory, SIAM Journal on Numerical Analysis, 44(1), pp. 367-384, 2006
  19. A. Quarteroni, G. Rozza, Numerical solution of parametrized Navier-Stokes equations by reduced basis methods, Numerical Methods for Partial Differential Equations, 23(4), pp. 923-948, 2007
  20. L. Formaggia, A. Moura, F. Nobile, On the stability of the coupling of 3D and 1D fluid-structure interaction models for blood flow simulations, Mathematical Modelling and Numerical Analysis, 41(4), pp.743–769, 2007
  21. F. Migliavacca, F. Gervaso, M. Prosi, P. Zunino, S. Minisini, L. Formaggia, G. Dubini, Expansion and drug elution model of a coronary stent, Comput. Methods. Biomech. Biomed. Engin., 10(1), pp. 63-73, 2007
  22. Vergara C., Zunino P., Multiscale modeling and simulation of drug release from cardiovascular stents, SIAM Multiscale Modeling and Simulation, 7(2), pp. 565-588, 2008
  23. Zunino P., D’Angelo C., Petrini L., Vergara C., Capelli C., Migliavacca F., Numerical simulation of drug eluting coronary stents: mechanics, fluid dynamics and drug release, Comp. Meth. Appl. Mech. Eng., 198(45-46), pp. 3633-3644, 2009
  24. L. Formaggia, S. Minisini, P. Zunino, Modeling erosion controlled drug release and transport phenomena in the arterial tissue, Math. Mod. Meth. Appl. Sciences, 20(10), pp.1759-1786, 2010
  25. L. Formaggia, S. Minisini, P. Zunino, Stent a rilascio di farmaco: una storia di successo per la matematica applicata, La Matematica nella Società e nella Cultura (Rivista della Unione Matematica Italiana), III, 181-200, 2010
  26. Vergara C., Ponzini R., Veneziani A., Redaelli A., Neglia D., Parodi O., Womersley number-based estimation of flow rate with Doppler Ultrasound: Sensitivity analysis and first clinical application, Computer Methods and Programs in Biomedicine, 98(2), pp. 151-160, 2010
  27. Ponzini R., Vergara C., Rizzo G., Veneziani A., Roghi A., Vanzulli A., Parodi O., Redaelli A., Womersley number-based estimates of blood flow rate in Doppler analysis: In vivo validation by means of Phase Contrast Magnetic Resonance Imaging, IEEE Transaction on Biomedical Engineering, 57 (7), pp. 1807-1815, 2010
  28. C. D’Angelo, P. Zunino, A. Porpora, S. Morlacchi, F. Migliavacca, Model reduction strategies enable computational analysis of controlled drug release from cardiovascular stents, SIAM J. Appl. Math., Special Issue on Mathematical Modeling of Controlled Drug Delivery, 71(6), pp. 2312-2333, 2011
  29. C. D’Angelo, P. Zunino, Numerical approximation with Nitsche’s coupling of transient Stokes/Darcy’s flow problems applied to hemodynamics, Appl. Num. Math., 62(4), pp. 378-95, 2011
  30. C. D’Angelo, P. Zunino, Robust numerical approximation of coupled Stokes and Darcy flows applied to vascular hemodynamics and biochemical transport, ESAIM: Mathematical Modelling and Numerical Analysis (M2AN), 45(3), pp. 447-476, 2011
  31. G. Pena, C. Prud’homme, A. Quarteroni, High order methods for the approximation of the incompressible Navier-Stokes equations in a moving domain, Computer Methods In Applied Mechanics And Engineering, 209, pp. 197-211, 2012
  32. L. Iapichino, A. Quarteroni, G. Rozza, A reduced basis hybrid method for the coupling of parametrized domains represented by fluidic networks, Computer Methods in Applied Mechanics and Engineering, 221-222, pp. 63-82, 2012
  33. A. Manzoni, A. Quarteroni, G. Rozza, Shape optimization for viscous flows by reduced basis methods and free-form deformation, International Journal for Numerical Methods in Fluids, 70, pp. 646-670, 2012
  34. A. Manzoni, A. Quarteroni, G. Rozza, Model reduction techniques for fast blood flow simulation in parametrized geometries, International Journal for Numerical Methods in Biomedical Engineering, 28, pp. 604-625, 2012
  35. T. M. Lassila, A. Manzoni, A. Quarteroni, G. Rozza, A reduced computational and geometrical framework for inverse problems in haemodynamics, International Journal Numerical Methods Biomedical Engineering, 29(7), pp. 741-776, 2013
  36. V. Anaya, D. Mora and R. Ruiz-Baier. An augmented mixed finite element method for the vorticity-velocity-pressure formulation of the Stokes equations, in Computer Methods In Applied Mechanics And Engineering, vol. 267, p. 261-274, 2013
  37. T. M. Lassila, A. Manzoni, A. Quarteroni, G. Rozza, Boundary control and shape optimization for the robust design of bypass anastomoses under uncertainty, Mathematical Modelling and Numerical Analysis, 47(4), pp. 1107-1131, 2013
  38. S. Deparis, G. Grandperrin, A. Quarteroni, Parallel preconditioners for the unsteady Navier-Stokes equations and applications to hemodynamics simulations, Computers & Fluids, 92, pp. 253-273, 2014
  39. Lancellotti R.M.. Vergara C., Valdettaro L., Bose S., Quarteroni A., Large Eddy Simulations for blood fluid-dynamics in real stenotic carotids. MOX Report n. 63/2015
  40. M. Benzi, S. Deparis, G. Grandperrin and A. Quarteroni. Parameter estimates for the Relaxed Dimensional Factorization preconditioner and application to hemodynamics, in Computer Methods in Applied Mechanics and Engineering, vol. 300, num. 1, p. 129-145, 2016.
  41. Guerciotti B., Vergara C., Computational comparison between Newtonian and non-Newtonian blood rheologies in stenotic vessels. MOX Report n. 19/2016.

 

Thesis:

  1. G. Rozza – Controllo Ottimale e ottimizzazione di forma in fluidodinamica computazionale, MSc in Aerospace Engineering – Advisor: A. Quarteroni – A.Y. ’02-’03
  2. E. Arcidiacono – Studio delle configurazioni di buckling di un modello di vaso sanguigno sottoposto a torsione e della sua influenza nella emodinamica – BSc in Mathematical Engineering – Advisor: L. Formaggia – A.Y. ’03-’04
  3. A. Invernizzi – Studio delle configurazioni di buckling di un modello di vaso sanguigno sottoposto a torsione e della sua influenza nella emodinamica – BSc in Mathematical Engineering – Advisor: L. Formaggia – A.Y. ’03-’04
  4. M. Perego – Modellazione matematica e numerica di problemi di ischemia cerebrale – MSc in Mathematical Engineering – Advisor: A. Veneziani – A.Y. ’03-’04
  5. M. De Luca – Modellazione matematico-numerica del Circolo di Willis – MSc in Biomedical Engineering – Advisor: A. Veneziani – A.Y. ’04-’05
  6. L. Toppeta – Simulazione numerica della circolazione sanguigna prima e dopo la nascita – BSc in Mathematical Engineering – Advisor: A. Veneziani – A.Y. ’04-’05
  7. E. Di Venosa – Simulazione numerica della circolazione sanguigna prima e dopo la nascita – BSc in Mathematical Engineering – Advisor: A. Veneziani – A.Y. ’04-’05
  8. F. Storti – Simulazione numerica della circolazione sanguigna neonatale in caso di ipoplasia del ventricolo sinistro – BSc in Mathematical Engineering – Advisor: A. Veneziani – A.Y. ’05-’06
  9. A. Porpora – Simulazione numerica della circolazione sanguigna neonatale in caso di ipoplasia del ventricolo sinistro – BSc in Mathematical Engineering – Advisor: A. Veneziani – A.Y. ’05-’06
  10. E. Maculan – Simulazioni fluidodinamiche in vasi deformabili con moto della parete ricostruito da immagini mediche – MSc in Mathematical Engineering- Advisor: A. Veneziani – A.Y. ’06-’07
  11. M. Martello – Metodi evolutivi per il rilascio di farmaco in protesi endovascolari – MSc in Mathematical Engineering- Advisor: P. Zunino – A.Y. ’06-’07
  12. R. Giacomini – Autoregulation models for cerebral haemodynamics – MSc in Aerospace Engineering – Advisor: L. Formaggia – A.Y. ’07-’08
  13. S. Minisini – Mathematical and Numerical Modeling of Controlled Drug Release – Ph.D. thesis in Mathematical Engineering – Advisor: L. Formaggia – A.Y. ’09-’10
  14. A. E. Andersson – Estimation of the compliance of the arterial walls through Kalman filtering – MSc in Mathematical Engineering – Advisor: L. Formaggia – A.Y. ’10-’11
  15. N. Chiappin – Analisi di sensitività dello sforzo a parete in applicazioni emodinamiche – MSc in Mathematical Engineering – Advisor: F. Nobile – A.Y. ’10-’11
  16. B. Guerciotti – Computational Comparison of Haemodynamics in Carotid Arteries before and after Endarterectomy – MSc in Mathematical Engineering – Advisor: F. Nobile – A.Y. ’13-’14