Fig. \[complete\_setup\]. It is worth mentioning that only one of the aorta and atrium exist in the geometry at the same time (the aorta just exist during the systole phase and will be removed during diastole and an opposite pattern for left atrium).

The blood flow flux from the left atrium and aorta to/from the LV chamber is specified based on the volumetric change of the LV (The volumetric flux of LV is calculated based on the change of LV volume in two consecutive time steps). In addition, the velocity boundary condition at the inlet of the atrium is assumed to be uniform. The Navier-Stocks equation is non-dimensionalized with a diameter, $D = 16.38 ~mm$, of the aortic orifice and the bulk velocity, $U = 0.598~m/s$, with a time step $dt = 0.0109~s$ over 2500 time instances during a cardiac cycle. Considering the blood viscosity to be $\nu= 3.3\times 10^{-6} m^2/s$ leads to a Reynold’s number of 2950 for the simulations. The LV geometry is discretized with approximately $50,000$ unstructured triangular mesh points and is immersed in a background grid with a dimension of $5.19D \times 3.33D \times 6.32D$ (where $D$ is the aortic diameter) discretized with $161 \times 121 