In this paper we present a collection of techniques used to formulate a projection-based reduced order model (ROM) for zero Mach limit thermally coupled Navier–Stokes equations. The formulation derives from a standard proper orthogonal decomposition (POD) model reduction, and includes modifications to improve the drawbacks caused by the inherent non-linearity of the used Navier–Stokes equations: a hyper-ROM technique based on mesh coarsening; an implicit ROM subscales formulation based on a variational multi-scale (VMS) framework; and a Petrov–Galerkin projection necessary in the case of non-symmetric terms. At the end of the article, we test the proposed ROM formulation using 2D and 3D versions of the same example: a differentially heated cavity.

中文翻译：

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热耦合低马赫流量的降阶模型

在本文中，我们介绍了用于为零马赫极限热耦合Navier–Stokes方程建立基于投影的降阶模型（ROM）的技术集合。该公式源自标准的适当正交分解（POD）模型简化，并进行了改进，以改善所使用的Navier-Stokes方程固有的非线性所引起的缺陷：基于网格粗化的Hyper-ROM技术；基于变分多尺度（VMS）框架的隐式ROM子尺度表示；对于非对称项，则需要Petrov-Galerkin投影。在本文的结尾，我们使用同一示例的2D和3D版本测试了建议的ROM配方：差热腔。