On the stability of projection-based model order reduction for convection-dominated laminar and turbulent flows
On the stability of projection-based model order reduction for convection-dominated laminar and turbulent flows
复制标题
对流主导的层流和湍流基于投影的模型降阶的稳定性
DOI：
10.1016/j.jcp.2020.109681
复制
发表时间：
2020
期刊：
影响因子：
--
通讯作者：
Noah Youkilis
中科院分区：
文献类型：
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作者：
Sebastian Grimberg;C. Farhat;Noah Youkilis
在计算流体动力学问题的基于非线性投影模型降阶的文献中，经常声称由于模态截断，基于投影的降阶模型（PROM）不能解决湍流能量级联的耗散状态，因此在数值上是不稳定的。解决这一问题的努力范围从试图模拟截断模态的影响到丰富经典的近似子空间，以解释截断现象。本文的目的是挑战这一说法。本文探讨了基于投影的模型降阶和半离散化之间的关系，并利用三个相关流动问题的数值证据，有序地论证了在湍流和对流主导的湍流问题中，大多数（如果不是全部）已报道的PROMs数值不稳定性背后的真正罪魁祸首是用于构建PROMs的伽辽金框架。本文还表明，Petrov-Galerkin框架可以用于构造对流占主导地位的层流和湍流问题的数值稳定和精确的PROMs，而无需借助额外的闭包模型或裁剪近似的子空间。它还表明，这种替代prom提供了显著的加速因素。
In the literature on nonlinear projection-based model order reduction for computational fluid dynamics problems, it is often claimed that due to modal truncation, a projection-based reduced-order model (PROM) does not resolve the dissipative regime of the turbulent energy cascade and therefore is numerically unstable. Efforts at addressing this claim have ranged from attempting to model the effects of the truncated modes to enriching the classical subspace of approximation in order to account for the truncated phenomena. The objective of this paper is to challenge this claim. Exploring the relationship between projection-based model order reduction and semi-discretization and using numerical evidence from three relevant flow problems, this paper argues in an orderly manner that the real culprit behind most if not all reported numerical instabilities of PROMs for turbulence and convection-dominated turbulent flow problems is the Galerkin framework that has been used for constructing the PROMs. The paper also shows that alternatively, a Petrov-Galerkin framework can be used to construct numerically stable and accurate PROMs for convection-dominated laminar as well as turbulent flow problems, without resorting to additional closure models or tailoring of the subspace of approximation. It also shows that such alternative PROMs deliver significant speed-up factors.