On-the-fly Reduced Order Modeling of Passive and Reactive Species via Time-Dependent Manifolds
On-the-fly Reduced Order Modeling of Passive and Reactive Species via Time-Dependent Manifolds
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DOI：
10.1016/j.cma.2021.113882
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发表时间：
2021-01
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影响因子：
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通讯作者：
Donya Ramezanian;A. Nouri;H. Babaee
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作者：
Donya Ramezanian;A. Nouri;H. Babaee
在具有大量物种的湍流中开发准确和易处理的预测模型的主要障碍之一是通过求解单独的输运方程来跟踪每个物种，这在计算上是不可行的。在本文中，我们提出了一种非飞行降阶模型的反应式和被动式输运方程，以降低计算成本。该方法寻求物种的低阶分解为三个依赖于时间的分量：(I)一组正交化空间模式，(Ii)瞬时物种关联矩阵的低阶分解，以及(Iii)一组代表低维依赖于时间的流形的正交化物种模式。我们的方法不需要求解全维物种来生成高保真数据-这在主成分分析等数据驱动的降维技术中通常是执行的。取而代之的是，低阶组分直接从物种传输方程中提取。从变分原理的最优性条件出发，得到了三组分的演化方程。这三个组分的时间依赖性使得低级分解能够在飞行中适应物种的瞬时变化。给出了被动输运方程和反应性输运方程降阶建模的几个实例。
One of the principal barriers in developing accurate and tractable predictive models in turbulent flows with a large number of species is to track every species by solving a separate transport equation, which can be computationally impracticable. In this paper, we present anon-the-flyreduced order modeling of reactive as well as passive transport equations to reduce the computational cost. The presented approach seeks a low-rank decomposition of the species to three time-dependent components: (i) a set of orthonormal spatial modes, (ii) a low-rank factorization of the instantaneous species correlation matrix, and (iii) a set of orthonormal species modes, which represents a low-dimensionaltime-dependent manifold. Our approach bypasses the need to solve the full-dimensional species to generate high-fidelity data — as it is commonly performed in data-driven dimension reduction techniques such as the principle component analysis. Instead, the low-rank components are directly extracted from the species transport equation. The evolution equations for the three components are obtained from optimality conditions of a variational principle. The time-dependence of the three components enables an on-the-fly adaptation of the low-rank decomposition to transient changes in the species. Several demonstration cases of reduced order modeling of passive and reactive transport equations are presented.