Efficient numerical solution of multiphysics hemodynamic problems
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We present here some examples of efficient numerical solutions related to problems in the field of hemodynamics. We first consider a new block preconditioner for the solution of incompressible fluids with flow rate defective boundary conditions in the framework of a Lagrange multipliers approach [1]. We show the effectiveness of the proposed method by means of several numerical experiments arising in realistic hemodynamic scenarios. Secondly, we present new results about the numerical solution of the fluid-structure interaction problem with large added mass. In particular, we introduce (conditionally-)stable loosely-coupled schemes, we provide the stability analysis for a model problem, and we present results of some numerical experiments in the hemodynamic regime. Finally, we consider a new cardiac perfusion model for the non-invasive prediction of blood flow maps at the myocardial level, based on the multiphysics nature of the coronary/microcirculation tree [2]. We discuss the efficient coupling between coronary and microcirculation blood flow and the challenging issue of the calibration to describe personalized conditions of patients. REFERENCES [1] L. Crugnola and C. Vergara, Inexact block LU preconditioners for incompressible fluids with flow rate conditions, arXiv, DOI:arXiv:2411.03929, (2024). [2] G. Montino Pelagi et al, Modeling cardiac microcirculation for the simulation of coronary flow and 3D myocardial perfusion, Biomech. Model. Mechanobiol., 23, 1863-1888, (2024).