Model order reduction of hemodynamics by space-time reduced basis and reduced fluid-structure interaction

TL;DR

This paper introduces an advanced space-time reduced basis method for simulating arterial blood flow, incorporating fluid-structure interaction and nonlinear dynamics to improve computational efficiency and accuracy.

Contribution

It extends the classical reduced basis method by integrating space-time encoding, modeling blood vessel elasticity, and implementing hyper-reduction for nonlinearities in hemodynamics simulations.

Findings

ST-GRB outperforms classical RB in accuracy and efficiency

Effective handling of nonlinear Navier-Stokes equations with hyper-reduction

Computational gains diminish with increasing temporal modes for complex dynamics

Abstract

In this work, we apply the space-time Galerkin reduced basis (ST-GRB) method to a reduced fluid-structure interaction model, for the numerical simulation of hemodynamics in arteries. In essence, ST-GRB extends the classical reduced basis (RB) method, exploiting a data-driven low-dimensional linear encoding of the temporal dynamics to further cut the computational costs. The current investigation brings forth two key enhancements, compared to previous works on the topic. On the one side, we model blood flow through the Navier-Stokes equations, hence accounting for convection. In this regard, we implement a hyper-reduction scheme, based on approximate space-time reduced affine decompositions, to deal with nonlinearities effectively. On the other side, we move beyond the constraint of modelling blood vessels as rigid structures, acknowledging the importance of elasticity for the accurate simulation of complex blood flow patterns. To limit computational complexity, we adopt the Coupled Momentum model, incorporating the effect of wall compliance in the fluid's equations through a generalized Robin boundary condition. In particular, we propose an efficient strategy for handling the spatio-temporal projection of the structural displacement, which ultimately configures as a by-product. The performances of ST-GRB are assessed in three different numerical experiments. The results confirm that the proposed approach can outperform the classical RB method, yielding precise approximations of high-fidelity solutions at more convenient costs. However, the computational gains of ST-GRB vanish if the number of retained temporal modes is too large, which occurs either when complex dynamics arise or if very precise solutions are sought.