Reduced order models for fluid-structure interaction problems with applications in haemodynamics

TL;DR

This paper introduces a two-level reduced order modeling approach combining mathematical reformulation and numerical techniques to enable fast, accurate simulations of fluid-structure interactions in large arteries, significantly reducing computational costs.

Contribution

The paper presents a novel combined reduction method using proper orthogonal decomposition and greedy algorithms for efficient haemodynamics simulations.

Findings

Achieved three orders of magnitude CPU time reduction.

Validated the method on realistic haemodynamics problems.

Demonstrated accurate results with reduced computational effort.

Abstract

This paper deals with fast simulations of the haemodynamics in large arteries by considering a reduced model of the associated fluid-structure interaction problem, which in turn allows an additional reduction in terms of the numerical discretisation. The resulting method is both accurate and computationally cheap. This goal is achieved by means of two levels of reduction: first, we describe the model equations with a reduced mathematical formulation which allows to write the fluid-structure interaction problem as a Navier-Stokes system with non-standard boundary conditions; second, we employ numerical reduction techniques to further and drastically lower the computational costs. The numerical reduction is obtained coupling two well-known techniques: the proper orthogonal decomposition and the reduced basis method, in particular the greedy algorithm. We start by reducing the numerical dimension of the problem at hand with a proper orthogonal decomposition and we measure the system energy with specific norms; this allows to take into account the different orders of magnitude of the state variables, the velocity and the pressure. Then, we introduce a strategy based on a greedy procedure which aims at enriching the reduced discretization space with low offline computational costs. As application, we consider a realistic haemodynamics problem with a perturbation in the boundary conditions and we show the good performances of the reduction techniques presented in the paper. The gains obtained in term of CPU time are of three orders of magnitude.