Model order reduction of flow based on a modular geometrical approximation of blood vessels

TL;DR

This paper introduces a modular geometrical approximation method for blood flow simulation that significantly reduces computational costs while maintaining accuracy, using domain decomposition and spectral basis functions derived from proper orthogonal decomposition.

Contribution

The paper presents a novel reduced order modeling approach combining domain decomposition with spectral basis functions for efficient blood flow simulation.

Findings

Achieves at least tenfold speedup compared to full simulations.

Maintains satisfactory accuracy in cardiovascular flow modeling.

Reduces the size of the linear systems in Newton-Raphson iterations.

Abstract

We are interested in a reduced order method for the efficient simulation of blood flow in arteries. The blood dynamics is modeled by means of the incompressible Navier-Stokes equations. Our algorithm is based on an approximated domain-decomposition of the target geometry into a number of subdomains obtained from the parametrized deformation of geometrical building blocks (e.g. straight tubes and model bifurcations). On each of these building blocks, we build a set of spectral functions by proper orthogonal decomposition of a large number of snapshots of finite element solutions (offline phase). The global solution of the Navier-Stokes equations on a target geometry is then found by coupling linear combinations of these local basis functions by means of spectral Lagrange multipliers (online phase). Being that the number of reduced degrees of freedom is considerably smaller than their finite element counterpart, this approach allows us to significantly decrease the size of the linear system to be solved in each iteration of the Newton-Raphson algorithm. We achieve large speedups with respect to the full order simulation (in our numerical experiments, the gain is at least of one order of magnitude and grows inversely with respect to the reduced basis size), whilst still retaining satisfactory accuracy for most cardiovascular simulations.