European Numerical Mathematics and
Advanced Applications Conference 2019
30th sep - 4th okt 2019, Egmond aan Zee, The Netherlands
10:40   MS36: Data-Driven Computational Fluid Dynamics (Part 2)
Chair: Alfonso Caiazzo
25 mins
Segregated methods for Reduced Order Models applied to the Navier-Stokes problem in a finite volume environment
Matteo Zancanaro, Giovannni Stabile, Gianluigi Rozza
Abstract: In fluid dynamics field the pressure stabilisation issue is a well known problem. Since this is a matter that occurs both at the Full Order and at the Reduced Order levels, several different strategies have been developed in order to overtake the obstacle. In our work we look at obtaining a new path towards the right solution without a proper stabilisation method. In particular the idea is to follow the common segregated algorithms, which are quite widespread in almost all finite volume solvers, also at the reduced level so that it is possible to have both a stable pressure recovery and a coherent reduced procedure at the same time (Ref 1). In this work we present the details about this procedure and we show some results obtained by its application. In particular also some comparisons between this architecture and some different other stabilisation techniques (Ref 2) will be exposed. (Ref 1) Stabile G., Zancanaro M., Rozza G., Efficient Geometrical parametrization for finite-volume based reduced order methods, submitted, (2019). (Ref 2) Stabile G., Rozza G., Finite volume POD-Galerkin stabilised reduced order methods for the parametrised incompressible Navier–Stokes equations, Computers & Fluids, 2018.
25 mins
3D flow reconstruction from Doppler ultrasound data
Felipe Galarce, Jean-Frédéric Gerbeau, Damiano Lombardi, Olga Mula
Abstract: Doppler echography is one of the most commonly used measurement modalities of blood flow in clinical applications. It is cheap and non-invasive. A number of decisions are made based on this kind of measurement. Of the available data, only a small portion is actually used in order to infer useful parameters characterizing the blood flow and the quantities of interest. Based on the theoretical results in [1], a numerical method is proposed in order to reconstruct the 3D flow in realistic geometries starting from Doppler velocimetry data. Ultrasound measurements are modeled. These can be seen, with a good approximation, as linear forms applied to the flow, so that the problem can be formulated as follows: given a set of linear forms applied to the flow, what is the best way to reconstruct the flow? The flow reconstruction is performed using an algorithm which assumes that the patient velocity belongs to a space containing a set of functions constrained by some governing equations. Furthermore, the more relevant information of this space is compressed into a set of basis in order to hugely improve the time-consumption of the method. The choice of a good and systematic way to build those bases is a topic by itself and we cover in this presentation a comparison between old and novel techniques to achieve this goal. A mathematical analysis is shown. In order to assess the performances of the proposed method, some numerical experiments are proposed, on synthetic geometries and in a more realistic case, on patient carotid arteries data. In the field of medicine, modern diagnostics and therapy optimization, the contribution of this work relays on its potential to predict quantities of interest from the reconstructed field, such as pressure gradients, flow and wall shear stress. We present the capabilities of our method to compute some of these quantities. [1] Binev, Peter and Cohen, Albert and Dahmen, Wolfgang and DeVore, Ronald and Petrova, Guergana and Wojtaszczyk, Przemyslaw. Data assimilation in reduced modeling. SIAM-ASA Journal on Uncertainty Quantification. 2017.
25 mins
Reducing the impact of geometrical errors in flow computations by assimilation of velocity data
Cristobal Bertoglio, David Nolte
Abstract: Numerical blood flow simulations are typically set up from anatomical medical images and calibrated using velocity measurements. However, the accuracy of the computational geometry itself is limited by the resolution of the anatomical image. We first show that applying standard no-slip boundary conditions on inaccurately extracted boundaries can cause large errors in the results, in particular the pressure gradient. In this talk, we therefore propose to augment the flow model calibration by slip/transpiration boundary conditions, whose parameters are then estimated using velocity measurements by means of the solution of an inverse problem. Numerical experiments show that this methodology can considerably improve the accuracy of the estimated pressure gradients and 3D velocity fields when the vessel geometry is uncertain.
25 mins
Data assimilation in one-dimensional hemodynamics
Alfonso Caiazzo
Abstract: One-dimensional (1D) models of blood flow represent an effective approach to obtain valuable insight inside the cardiovascular system (i.e., arterial parameters) with a much computational effort, with respect to full (3D) fluid models. This talk overview recent results concerning data assimilation methods combining 1D hemodynamics models (for the forward problem) and a reduced-order unscented Kalman filter for the solution the inverse problem related to parameter estimation. In particular, we employ a high order finite volume method, combined with a local-time stepping scheme, to efficiently and robustly solve the one-dimensional flow. Assuming quasi-periodicity of the forward model, the Kalman filter is applied in frequency domain, correcting parameter estimates after each hearth beat. We show preliminary results using in vitro and in vivo data, as well as potential applications combining this approach with further model-order reduction methods.