In this paper, we investigate the haemodynamics of a left atrium (LA) by proposing a computational model suitable to provide physically meaningful fluid dynamics indications and detailed blood flow characterization. In particular, we consider the incompressible Navier–Stokes equations in Arbitrary Lagrangian Eulerian (ALE) formulation to deal with the LA domain under prescribed motion. A Variational Multiscale (VMS) method is adopted to obtain a stable formulation of the Navier–Stokes equations discretized by means of the Finite Element method and to account for turbulence modelling based on Large Eddy Simulation (LES). The aim of this paper is twofold: on one hand to improve the general understanding of blood flow in the human LA in normal conditions; on the other, to analyse the effects of the turbulence VMS-LES method on a situation of blood flow which is neither laminar, nor fully turbulent, but rather transitional as in LA. Our results suggest that if relatively coarse meshes are adopted, the additional stabilization terms introduced by the VMS-LES method allow to better predict transitional effects and cycle-to-cycle blood flow variations than the standard SUPG stabilization method.

在本文中，我们通过提出一种计算模型来研究左心房 (LA) 的血流动力学，该模型适用于提供具有物理意义的流体动力学指示和详细的血流表征。特别是，我们考虑了任意拉格朗日欧拉 (ALE) 公式中的不可压缩 Navier-Stokes 方程来处理规定运动下的 LA 域。采用变分多尺度 (VMS) 方法来获得通过有限元方法离散化的 Navier-Stokes 方程的稳定公式，并考虑基于大涡模拟 (LES) 的湍流建模。本文的目的有两个：一方面提高对正常情况下人体 LA 血流的一般认识；在另一，分析湍流 VMS-LES 方法对既不是层流也不是完全湍流的血流情况的影响，而是像 LA 那样过渡。我们的结果表明，如果采用相对较粗的网格，与标准 SUPG 稳定方法相比，VMS-LES 方法引入的附加稳定项可以更好地预测过渡效应和循环到循环的血流变化。