An oscillation-free fully staggered algorithm for velocity-dependent active models of cardiac mechanics
An oscillation-free fully staggered algorithm for velocity-dependent active models of cardiac mechanics
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DOI：
10.1016/j.cma.2020.113506
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发表时间：
2021-01-01
影响因子：
7.2
通讯作者：
Quarteroni, A.
中科院分区：
文献类型：
--
作者：
Regazzoni, F.;Quarteroni, A.
在本文中，我们解决了一个悬而未决的问题，在心脏电动力学的数值模拟，即发病的数值振荡，由于依赖的力产生模型的纤维缩短速度。避免数值振荡的一种方法是使用整体格式来求解主被动力学的耦合问题。然而，交错的策略，预见力的产生和组织力学的模型的顺序解决方案，是优选的，由于其降低的计算成本和低的实施工作。在本文中，我们提出了解决这个问题的方法，即针对标准交错格式引入一个数值一致的稳定项。这一术语是由于识别宏观和微观应变之间不匹配的不稳定性原因而得出的，分别以拉格朗日和欧拉坐标表示。通过考虑主动力学的模型问题，我们证明了所提出的计划是无条件绝对稳定的（即它是稳定的任何时间步长），但在一个完全交错的框架。因此，新方案消除了非物理振荡，因为我们证明了它应用到三个力生成模型，即Niedererer-Hunter-Smith模型，模型的土地和同事，以及平均场力生成模型，我们最近提出的。(C)2020作者（S）由爱思唯尔公司出版
In this paper we address an unresolved problem in the numerical modeling of cardiac electromechanics, that is the onset of numerical oscillations due to the dependence of force generation models on the fibers shortening velocity. A way to avoid numerical oscillations is to use monolithic schemes for the solution of the coupled problem of active-passive mechanics. However, staggered strategies, which foresee the sequential solution of the models of force generation and of tissue mechanics, are preferable, due to their reduced computational cost and low implementation effort. In this paper we propose a cure for this issue, by introducing, with respect to the standard staggered scheme, a numerically consistent stabilization term. This term is derived in virtue of the identification of the cause of instability in the mismatch between macroscopic and microscopic strains, inconsistently expressed in Lagrangian and Eulerian coordinates, respectively. By considering a model problem of active mechanics we prove that the proposed scheme is unconditionally absolutely stable (i.e. it is stable for any time step size), yet within a fully staggered framework. As such, the new scheme removes the non-physical oscillations, as we prove by applying it to three force generation models, namely the Niederer-Hunter-Smith model, the model by Land and coworkers, and the mean-field force generation model that we have recently proposed. (C) 2020 The Author(s). Published by Elsevier B.V.