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.

在针对计算流体动力学问题的基于非线性投影的模型降阶的文献中，通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，并且因此在数值上是不稳定的。解决这一要求的努力范围从尝试对截断模式的影响建模到丰富经典的近似子空间以解决截断现象，不一而足。本文的目的是挑战这一主张。探索基于投影的模型降阶和半离散化之间的关系，并使用来自三个相关流动问题的数值证据，本文以有序的方式指出，大多数（如果不是全部）所报告的PROM湍流和对流主导的湍流问题的数值不稳定性背后的真正罪魁祸首是用于构造PROM的Galerkin框架。本文还表明，也可以使用Petrov-Galerkin框架构造对流占优势的层流以及湍流​​问题的数值稳定且精确的PROM，而无需诉诸其他封闭模型或定制近似子空间。它还表明，此类替代PROM具有显着的加速因素。Petrov-Galerkin框架可用于构造对流占主导的层流以及湍流​​问题的数值稳定且精确的PROM，而无需求助于其他闭合模型或定制近似子空间。它还表明，此类替代PROM具有显着的加速因素。Petrov-Galerkin框架可用于构造对流占主导的层流以及湍流​​问题的数值稳定且精确的PROM，而无需求助于其他闭合模型或定制近似子空间。它还表明，此类替代PROM具有显着的加速因素。