  We present a new computational model for the numerical simulation of blood
flow in the human left heart. To this aim, we use the Navier-Stokes equations
in an Arbitrary Lagrangian Eulerian formulation to account for the endocardium
motion and we model the cardiac valves by means of the Resistive Immersed
Implicit Surface method. To impose a physiological displacement of the domain
boundary, we use a 3D cardiac electromechanical model of the left ventricle
coupled to a lumped-parameter (0D) closed-loop model of the remaining
circulation. We thus obtain a one-way coupled electromechanics-fluid dynamics
model in the left ventricle. To extend the left ventricle motion to the
endocardium of the left atrium and to that of the ascending aorta, we introduce
a preprocessing procedure according to which an harmonic extension of the left
ventricle displacement is combined with the motion of the left atrium based on
the 0D model. To better match the 3D cardiac fluid flow with the external blood
circulation, we couple the 3D Navier-Stokes equations to the 0D circulation
model, obtaining a multiscale coupled 3D-0D fluid dynamics model that we solve
via a segregated numerical scheme. We carry out numerical simulations for a
healthy left heart and we validate our model by showing that meaningful
hemodynamic indicators are correctly reproduced.
