A major challenge in the computational fluid dynamics modeling of the heart function is the simulation of isovolumetric phases when the hemodynamics problem is driven by a prescribed boundary displacement. During such phases, both atrioventricular and semilunar valves are closed: consequently, the ventricular pressure may not be uniquely defined, and spurious oscillations may arise in numerical simulations. In this paper, we propose a suitable modification of the Resistive Immersed Implicit Surface (RIIS) method (Fedele et al., 2017) by introducing a reaction term to correctly capture the pressure transients during isovolumetric phases. The method, that we call Augmented RIIS (ARIIS) method, extends the previously proposed ARIS method (This et al., 2020) to the case of a mesh which is not body-fitted to the valves. We test the proposed method on two different benchmark problems, including a new simplified problem that retains all the characteristics of a heart cycle. We apply the ARIIS method to a fluid dynamics simulation of a realistic left heart geometry, and we show that ARIIS allows to correctly simulate isovolumetric phases, differently from standard RIIS method.

翻译：心脏功能的计算流体动态模型中的一项重大挑战是当血动力学问题被规定的边界迁移驱动时,模拟异体体积阶段是一个主要的挑战。在这些阶段中,先生动阀门和半卢纳尔阀门都关闭了。因此,心血管压力可能不是独特的定义,在数字模拟中可能会出现虚假的振动。在本文件中,我们建议对坚忍的Immers Inmmercitimate Floor (RIIS) 方法(Fedele et al., 2017) 进行适当修改,方法是引入一个反应术语,以正确捕捉到等量阶段的压力中瞬态。我们称之为ARIIS (ARIIS) 方法的方法,将先前提议的ARIS 方法(Thiet al.,2020) 扩展至与阀体不相适应的网块的情况。我们建议对两种不同的基准问题进行测试,包括保留心脏循环所有特性的新的简化问题。我们将ARIIS 方法用于现实的左心血管动态动态模拟,我们正确地模拟了ARIIS 标准方法。