Efficient modeling of incompressible fluid dynamics at moderate Reynolds numbers by deconvolution LES Filters
Analysis and applications to hemodynamics
DMS-1620384 (UH) and DMS-1620406 (Emory)

Abstract

The Direct Numerical Simulation (DNS) of the Navier-Stokes equations computes the evolution of all the significant flow structures by resolving them with a properly refined mesh. Unfortunately, when the convection dominates the dynamics - as it happens in many practical applications - this requires very fine meshes, making DNS computationally unaffordable for practical purposes. In particular, we consider new and innovative applications of scientific computing in cardiovascular sciences. While proofs of concept of the relevance of a numerical quantitative analysis to the clinical practice for cardiovascular diseases are abundant, a massive use of scientific computing tools as a decision-making support for doctors still has to come. New groundbreaking concepts in Medicine like Computer Aided Clinical Trials (CACT) and Surgical Planning (SP) are expected to have a strong impact on healthcare, yet they need highly effective and reliable methods. In particular, when investigating a variety of aortic diseases and surgeries, the presence of highly disturbed flows rapidly increases the computational costs. This prevents the use of scientific computing in routine clinical practice. This proposal addresses the crucial need to find a valid alternative to DNS featuring reasonable computational times without sacrificing accuracy for incompressible flow at moderate Reynolds numbers (few thousands). We intend to investigate carefully new cutting-edge methods for disturbed flows based on Large Eddy Simulation (LES) Deconvolution filtering techniques with the ultimate goal of enabling practical use of numerical tools to improve knowledge extraction and clinical practice through CACT and SP.

Principal Investigators
Dr. A. Quaini, University of Houston
Dr. A. Veneziani, Emory University

Collaborators and Consultants
Dr. L. Rebholz, Clemson
Dr. G. Rozza, SISSA

Students Involved in the Project
Quang Hoang, Undergraduate student (UH)
Kaylie O'Connell, Undergraduate student (UH)
Kayla Bicol, Graduate student (UH)
Daewa Kim, Graduate student (UH)
Giuseppe Pitton, Graduate student (SISSA)
Krithika Rathinakumar, Graduate student (UH)
Huijuan Xu, Graduate student (Emory)
Steffen Basting, Post-Doc (TU Dortmund)
Luca Bertagna, Post-Doc (Sandia)
Michele Girfoglio, Post-Doc (SISSA)
Martin Hess, Post-Doc (SISSA)
Yifan Wang, Post-Doc (UH)
Vladimir Yushutin, Post-Doc (UH)

Publications

1. M. Girfoglio, A. Quaini, G. Rozza: A Hybrid Reduced Order Model for nonlinear LES filtering, Submitted.
   arXiv:2107.12933
2. D. Kim, A. Quaini: A 2D kinetic model for crowd dynamics with disease contagion, Submitted.
   arXiv:2107.11401
3. M. Girfoglio, A. Quaini, G. Rozza: Pressure stabilization strategies for a LES filtering Reduced Order Model, Fluids, 6(9): 302, 2021.
   arXiv:2106.15887 | link
4. Olshanskii, A. Quaini, Q. Sun: A finite element method for two-phase flow with material viscous interface, Submitted.
   arXiv:2106.02922
5. Y. Palzhanov, A. Zhiliakov, A. Quaini, and M. Olshanskii: A decoupled, stable, and linear FEM for a phase-field model of variable density two-phase incompressible surface flow, Comput. Methods Appl. Mech. Engrg., Accepted.
   arXiv:2104.08996
6. D. Kim, A. Quaini: A kinetic theory approach to model crowd dynamics with disease contagion. Accepted in: N. Bellomo, L. Gibelli (eds) Crowd Dynamics Volume 3 - Modeling and Social Applications. Modeling and Simulation in Science, Engineering and Technology, Birkhauser-Springer, 2021.
   arXiv:2103.15151
7. M. Girfoglio, A. Quaini, G. Rozza: Fluid-structure interaction simulations with a LES filtering approach in solids4Foam, Commun. Appl. Ind. Math.,12 (1): 13-28, 2021.
   arXiv:2102.08011 | link
8. Olshanskii, A. Quaini, Q. Sun: An unfitted finite element method for two-phase Stokes problems with slip between phases, J. Sci. Comput., Accepted.
   arXiv:2101.09627.
9. M. Hess, A. Quaini, G. Rozza: A comparison of reduced-order modeling approaches for PDEs with bifurcating solutions, Electron. Trans. Numer. Anal. (ETNA), Accepted.
   arXiv:2010.07370
10. M. Girfoglio, A. Quaini, G. Rozza: A POD-Galerkin reduced order model for a LES filtering approach, J. Comput. Phys., 436:110260, 2021.
    ariXiv:2009.13593 | link
11. D. Kim, K. O'Connell, W. Ott, A. Quaini: A kinetic theory approach for 2D crowd dynamics with emotional contagion, Math. Models Methods Appl. Sci., 31(6):1137-1162, 2021.
    arXiv:2012.08108 | link
12. A. Zhiliakov, Y. Wang, A. Quaini, M. Olshanskii, S. Majd: Experimental validation of a phase-field model to predict coarsening dynamics of lipid domains in multicomponent membranes, BBA - Biomembranes, 1863(1):183446, 2021.
    arXiv:2006.14125 | link
13. D. Kim, A. Quaini: Coupling kinetic theory approaches for pedestrian dynamics and disease contagion in a confined environment, Math. Models Methods Appl. Sci., D. Kim, A. Quaini: Coupling kinetic theory approaches for pedestrian dynamics and disease contagion in a confined environment, Math. Models Methods Appl. Sci., 30(10):1893-1915, 2020.
    arXiv:2003.08357 | link
14. K. Rathinakumar, A. Quaini: A microscopic approach to study the onset of a highly infectious disease spreading, Mathematical Biosciences, 329:108475, 2020.
    arXiv:2004.09554 | link
15. V. Yushutin, A. Quaini, M. Olshanskii: Numerical modelling of phase separation on dynamic surfaces, J. Comput. Phys., 407:109126, 2020.
    link | arXiv:1907.1131
16. H. Xu, F. Di Massimo, D. Baroli, A. Quaini, A. Veneziani: Backflow stabilization by deconvolution-based Large Eddy Simulation modeling, J. Comput. Phys., 404:109103, 2020.
    link
17. M. Hess, A. Quaini, G. Rozza: Reduced basis model order reduction for Navier-Stokes equations in domains with walls of varying curvature, Int. J. Comput. Fluid Dyn., 34(2):119-126, 2020.
    link | arXiv:1901.03708
18. M. Hess, A. Quaini, G. Rozza: A spectral element reduced basis method for Navier-Stokes equations with geometric variations, In: Sherwin S., Moxey D., Peiro' J., Vincent P., Schwab C. (eds) Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018. Lecture Notes in Computational Science and Engineering, vol 134, Springer Cham, 2020.
    link | arXiv:1812.11051
19. K. Bicol and A. Quaini: On the sensitivity to model parameters in a filter stabilization technique for advection dominated advection-diffusion-reaction problems, In: van Brummelen H., Corsini A., Perotto S., Rozza G. (eds) Numerical Methods for Flows. Lecture Notes in Computational Science and Engineering, vol 132. Springer, Cham.
    link |arXiv:1805.01376
20. M. Girfoglio, A. Quaini, G. Rozza: A Finite Volume approximation of the Navier-Stokes equations with nonlinear filtering stabilization, Computers and Fluids, 187:27-45, 2019.
    link | arXiv:1901.05251
21. V. Yushutin, A. Quaini, S. Majd, M. Olshanskii: A computational study of lateral phase separation in biological membranes, Int. J. Num. Meth. Biomed. Eng., 35(3):e3181, 2019.
    link | arXiv:1808.06741
22. M. Hess, A. Alla, A. Quaini, G. Rozza, M. Gunzburger: A localized reduced-order modeling approach for PDEs with bifurcating solutions, Comput. Methods Appl. Mech. Engrg., 351:379-403, 2019.
    link | arXiv:1807.08851
23. L. Bertagna, A. Quaini, L.G. Rebholz, A. Veneziani: On the sensitivity to the filtering radius in Leray models of incompressible flow, In: Chetverushkin B., Fitzgibbon W., Kuznetsov Y., Neittaanmäki P., Periaux J., Pironneau O. (eds) Contributions to Partial Differential Equations and Applications. Computational Methods in Applied Sciences, vol 47. Springer, Cham, pages 111-130, 2019.
    link | preprint
24. M. Olshanskii, A. Quaini, A. Reusken, V. Yushutin: A finite element method for the surface Stokes problem, SIAM J. Sci. Comput., 40(4):A2492-A2518, 2018.
    link | arXiv:1801.06589
25. Y. Wang, A. Quaini, S. Canic: A higher-order Discontinuous Galerkin/Arbitrary Lagrangian Eulerian partitioned approach to solving fluid-structure interaction problems with incompressible, viscous fluids and elastic structures, Accepted in J. Sci. Comput., 76(1):481-520, 2018.
    link | preprint
26. Y. Wang, A. Quaini, S. Canic, M. Vukicevic, S. Little: 3D experimental and computational analysis of eccentric mitral regurgitant jets in a mock imaging heart chamber, Cardiovascular Engineering and Technology, 8(4):419-438, 2017.
    link
27. D. Forti, M. Bukac, A. Quaini, S. Canic, S. Deparis: A monolithic approach to fluid-composite structure interaction, J. Sci. Comput., 72(1):396-421, 2017.
    link | preprint
28. G. Pitton, A. Quaini, G. Rozza: Computational reduction strategies for the detection of steady bifurcations in incompressible fluid-dynamics: Applications to Coanda effect in cardiology, J. Comput. Phys., 344:534-557, 2017.
    link | arXiv:1708.09718
29. S. Basting, A. Quaini, R. Glowinski, S. Canic: An extended ALE method for fluid-structure interaction problems with large structural displacements, J. Comput. Phys., 331:312-336, 2017.
    link | preprint
30. S. Basting, A. Quaini, R. Glowinski, S. Canic: On the implementation and benchmarking of an extended ALE Method for FSI problems, In Fluid-Structure Interaction: Modeling, Adaptive Discretizations and Solvers, S. Frei, B. Holm, T. Richter, T. Wick, H. Yang Eds., pages 3–39, 2017.
31. L. Shi, S. Canic, A. Quaini, T.-W. Pan: A study of self-propelled elastic cylindrical micro-swimmers using modeling and computation, J. Comput. Phys., 314:264-286, 2016.
    link | preprint
32. L. Bertagna, A. Quaini, A. Veneziani: Deconvolution-based nonlinear filtering for incompressible flows at moderately large Reynolds numbers, Int. J. Num. Meth. Fluids, 81(8):463-488, 2016.
    link | preprint
33. A. Cesmelioglu, H. Lee, A. Quaini, K. Wang, S.-Y. Yi: Optimization-based decoupling algorithms for a fluid-poroelastic system, Topics in Numerical Partial Differential Equations and Scientific Computing. In The IMA Volumes in Mathematics and its Applications, volume 160: 79-98, 2016.
    link | preprint

Reports
Year 1 (UH) - Year 2 (UH) - Year 3 (UH) - Year 4 (UH)

Software

The software used for the simulations in the above papers is:

• LifeV, distributed under the GNU Lesser General Public License.

• ITHACA-FV, freely available under the GPL 3 License.

• FEniCS, distributed under the GNU Lesser General Public License.

• DROPS, distributed under the GNU Lesser General Public License.