A stable loosely-coupled scheme for cardiac electro-fluid-structure interaction

TL;DR

This paper introduces a stable, loosely-coupled numerical scheme for cardiac electro-fluid-structure interaction that reduces computational costs while maintaining stability, offering an efficient alternative to implicit methods in large-scale cardiac simulations.

Contribution

The paper proposes an explicit Robin-Neumann algorithm for fluid-structure coupling in cardiac models, balancing accuracy and computational efficiency.

Findings

The scheme is stable under typical cardiac simulation regimes.

Computational times are significantly reduced compared to implicit schemes.

The explicit scheme offers a good trade-off between accuracy and computational cost.

Abstract

We present a loosely coupled scheme for the numerical simulation of the cardiac electro-fluid-structure interaction problem, whose solution is typically computationally intensive due to the need to suitably treat the coupling of the different submodels. Our scheme relies on a segregated treatment of the subproblems, in particular on an explicit Robin-Neumann algorithm for the fluid-structure interaction, aiming at reducing the computational burden of numerical simulations. The results, both in an ideal and a realistic cardiac setting, show that the proposed scheme is stable at the regimes typical of cardiac simulations. From a comparison with a scheme with implicit fluid-structure interaction, it emerges that, while conservation properties are not fully preserved, computational times significantly benefit from the explicit scheme. Overall, the explicit discretization represents a good trade-off between accuracy and cost, and is a valuable alternative to implicit schemes for fast large-scale simulations.