  Computational fluid dynamics (CFD) studies of left atrial flows have reached
a sophisticated level, e.g., revealing plausible relationships between
hemodynamics and stresses with atrial fibrillation. However, little focus has
been on fundamental fluid modelling of LA flows. The purpose of this study was
to investigate the spatiotemporal convergence, along with the differences
between high- (HR) versus normal-resolution/accuracy (NR) solution strategies,
respectively. CFD simulations on 12 patient-specific left atrial geometries,
obtained from computed tomography scans, were performed by using a second-order
accurate and space/time centered solver. The convergence studies showed an
average variability of around 30\% and 55\% for time averaged wall shear stress
(WSS), oscillatory shear index (OSI), relative residence time (RRT), and
endothelial cell activation potential (ECAP), even between intermediate spatial
and temporal resolutions, in the left atrium (LA) and left atrial appendage
(LAA), respectively. The comparison between HR and NR simulations showed good
correlation in the LA for WSS, RRT, and ECAP (R^2 > 0.9), but not for OSI (R^2
= 0.63). However, there were poor correlations in the LAA especially for OSI,
RRT, and ECAP (R^2 = 0.55, 0.63, and 0.61, respectively), except for WSS (R^2 =
0.81). The errors are comparable to differences previously reported with
disease correlations. To robustly predict atrial hemodynamics and stresses,
numerical resolutions of 10M elements and 10k time-steps per cycle seem
necessary (i.e., one order of magnitude higher than normally used in both space
and time). In conclusion, attention to fundamental numerical aspects is
essential towards establishing a plausible, robust, and reliable model of LA
flows.
