A velocity tracking approach for the Data Assimilation problem in blood flow simulations

TL;DR

This paper introduces a velocity control-based data assimilation method for blood flow simulations that improves accuracy in complex 3D geometries like brain aneurysms, reducing reliance on idealized boundary conditions.

Contribution

It presents a novel velocity control approach using a discretize-then-optimize method for blood flow data assimilation in complex geometries.

Findings

Improves accuracy over pressure control strategies

Effective in realistic 3D brain aneurysm models

Reduces dependence on idealized boundary conditions

Abstract

Several advances have been made in Data Assimilation techniques applied to blood flow modeling. Typically, idealized boundary conditions, only verified in straight parts of the vessel, are assumed. We present a general approach, based on a Dirichlet boundary control problem, that may potentially be used in different parts of the arterial system. The relevance of this method appears when computational reconstructions of the 3D domains, prone to be considered sufficiently extended, are either not possible, or desirable, due to computational costs. Based on taking a fully unknown velocity profile as the control, the approach uses a discretize then optimize methodology to solve the control problem numerically. The methodology is applied to a realistic 3D geometry representing a brain aneurysm. The results show that this DA approach may be preferable to a pressure control strategy, and that it can significantly improve the accuracy associated to typical solutions obtained using idealized velocity profiles.