Premium
Model reduction techniques for fast blood flow simulation in parametrized geometries
Author(s) -
Manzoni Andrea,
Quarteroni Alfio,
Rozza Gianluigi
Publication year - 2011
Publication title -
international journal for numerical methods in biomedical engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.741
H-Index - 63
eISSN - 2040-7947
pISSN - 2040-7939
DOI - 10.1002/cnm.1465
Subject(s) - parametrization (atmospheric modeling) , vorticity , parametric statistics , reduction (mathematics) , basis (linear algebra) , flow (mathematics) , mathematics , focus (optics) , navier–stokes equations , computational fluid dynamics , geometry , mathematical optimization , algorithm , computer science , mechanics , vortex , physics , statistics , quantum mechanics , compressibility , optics , radiative transfer
SUMMARY In this paper, we propose a new model reduction technique aimed at real‐time blood flow simulations on a given family of geometrical shapes of arterial vessels. Our approach is based on the combination of a low‐dimensional shape parametrization of the computational domain and the reduced basis method to solve the associated parametrized flow equations. We propose a preliminary analysis carried on a set of arterial vessel geometries, described by means of a radial basis functions parametrization. In order to account for patient‐specific arterial configurations, we reconstruct the latter by solving a suitable parameter identification problem. Real‐time simulation of blood flows are thus performed on each reconstructed parametrized geometry, by means of the reduced basis method. We focus on a family of parametrized carotid artery bifurcations, by modelling blood flows using Navier–Stokes equations and measuring distributed outputs such as viscous energy dissipation or vorticity. The latter are indexes that might be correlated with the assessment of pathological risks. The approach advocated here can be applied to a broad variety of (different) flow problems related with geometry/shape variation, for instance related with shape sensitivity analysis, parametric exploration and shape design. Copyright © 2011 John Wiley & Sons, Ltd.