Backflow stabilization by deconvolution-based large eddy simulation modeling
Backflow stabilization by deconvolution-based large eddy simulation modeling
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DOI：
10.1016/j.jcp.2019.109103
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发表时间：
2020-03
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影响因子：
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通讯作者：
Huijuan Xu;Francesca Di Massimo;D. Baroli;A. Quaini;A. Veneziani
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作者：
Huijuan Xu;Francesca Di Massimo;D. Baroli;A. Quaini;A. Veneziani
在不可压缩流体的数值模拟中，通过指定诺伊曼条件的出口边界出现的流入流可能会引入称为回流不稳定性的数值不稳定性。这种回流不稳定性与非线性对流项有关，并且常常对大血管中血流的数值模拟提出挑战。事实上，收缩期和舒张期的交替会引起出口处的回流，这通常是诺伊曼边界，因为缺乏速度数据需要指定牵引/压力条件。触发回流不稳定的雷诺数通常是中等的（在几百或以上的范围内）。在这项工作中，我们证明了一个特定的大涡模拟（LES）模型隐式地稳定了回流不稳定。该 LES 模型使用反卷积滤波器，是 Layton、Rebholz 及其合作者最近推出的所谓 Evolve-Filter-Relax 方案的基础，作为中等或大雷诺数流的直接数值模拟的有效替代方案。通过明智地选择该 LES 方案的参数，可以抑制触发数值回流不稳定的项，从而获得可靠且高效的数值模拟。这在计算临床研究中特别有吸引力，因为许多病例需要在相对较短的时间内进行研究。我们为我们的陈述提供了严格的证明，并提供了数字证据，证实了理想化和现实案例的理论。对于后者，我们考虑患者特定的主动脉瘤几何形状。主动脉模拟具有雷诺数和血流状态，特别受益于这种偶然（又名“两只鸟一石头”）的情况，其中 LES 建模正在稳定数值伪影。
In the numerical simulations of incompressible fluids, the occurrence of incoming flows through outlet boundaries where Neumann conditions are prescribed may introduce the numerical instability known as thebackflow instability. This backflow instability is related to the nonlinear convective term and is often challenging the numerical simulation of the blood flow in large vessels. In fact, the alternation of systole and diastole induces backflows at the outlets, which are usually Neumann boundaries since the lack of velocity data requires the prescription of traction/pressure conditions. The Reynolds numbers that trigger the backflow instability are generally moderate (in the range of a few hundreds and above).In this work, we prove that a particular Large Eddy Simulation (LES) model implicitly stabilizes the backflow instability. This LES model uses deconvolution filters and is the basis of the so-called Evolve-Filter-Relax scheme recently introduced by Layton, Rebholz and their collaborators as an effective alternative to Direct Numerical Simulations for the moderate or large Reynolds number flow. With a judicious selection of the parameters of this LES scheme, it is possible to suppress the term that triggers the numerical backflow instability, so to obtain reliable and efficient numerical simulations. This is particularly attractive in computational clinical studies, where many cases need to be studied in a relatively short time.We provide a rigorous proof of our statement and numerical evidence that corroborates the theory on both idealized and realistic cases. For the latter, we consider a patient-specific aortic aneurysm geometry. Aortic simulations feature Reynolds numbers and flow regimes that particularly benefit from thisserendipity(aka ‘two-birds-one-stone’) circumstance, where a LES modeling is stabilizing a numerical artifact.