论文标题
关于基于投影基于投影的模型订单的稳定性，以对流为主的层流和湍流
On the stability of projection-based model order reduction for convection-dominated laminar and turbulent flows
论文作者
论文摘要
在有关流体动力学问题的基于投影的非线性模型降低的文献中，通常声称由于模态截断，基于投影的基于投影的减少阶模型（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。解决这一主张的努力范围从试图建模截断模式的影响到丰富近似的经典子空间以说明截断现象的效果。本文挑战了这一主张。探索基于投影基于投影的模型订单减少和半差异之间的关系，并使用来自三个相关流问题的数值证据，它以有序的方式说明，大多数情况下，如果不是全部报告的大多数报道的蓬勃发展的数值不稳定性背后的罪魁祸首，则用于湍流和对流为主导的湍流问题，是用于构建Proms的Galerkin框架。该论文还表明，可以使用Petrov-Galerkin框架来构建数值稳定的舞会，以用于对流为主的层流以及湍流问题，这些问题在数值上稳定且准确，而无需求助于额外的闭合模型或对近似值的子空间的定制。它还表明，这种替代舞会提供了重要的加速因素。
In the literature on projection-based nonlinear model order reduction for 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. This paper challenges this claim. Exploring the relationship between projection-based model order reduction and semi-discretization and using numerical evidence from three relevant flow problems, it 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 PROMs for convection-dominated laminar as well as turbulent flow problems that are numerically stable and accurate, without resorting to additional closure models or tailoring of the subspace of approximation. It also shows that such alternative PROMs deliver significant speedup factors.
