This article provides a reduced-order modelling framework for turbulent compressible flows discretized by the use of finite volume approaches. The basic idea behind this work is the construction of a reduced-order model capable of providing closely accurate solutions with respect to the high fidelity flow fields. Full-order solutions are often obtained through the use of segregated solvers (solution variables are solved one after another), employing slightly modified conservation laws so that they can be decoupled and then solved one at a time. Classical reduction architectures, on the contrary, rely on the Galerkin projection of a complete Navier-Stokes system to be projected all at once, causing a mild discrepancy with the high order solutions. This article relies on segregated reduced-order algorithms for the resolution of turbulent and compressible flows in the context of physical and geometrical parameters. At the full-order level turbulence is modeled using an eddy viscosity approach. Since there is a variety of different turbulence models for the approximation of this supplementary viscosity, one of the aims of this work is to provide a reduced-order model which is independent on this selection. This goal is reached by the application of hybrid methods where Navier-Stokes equations are projected in a standard way while the viscosity field is approximated by the use of data-driven interpolation methods or by the evaluation of a properly trained neural network. By exploiting the aforementioned expedients it is possible to predict accurate solutions with respect to the full-order problems characterized by high Reynolds numbers and elevated Mach numbers.

翻译：本文提出了一种针对采用有限体积法离散的湍流可压缩流动的降阶建模框架。本工作的核心思想是构建一种降阶模型，使其能够提供相对于高保真流场高度精确的近似解。全阶解通常通过使用分离式求解器（逐个求解各变量）获得，其中对守恒定律进行适当修改，以实现方程解耦并逐一求解。相比之下，经典降阶架构依赖于对整个纳维-斯托克斯系统进行一次性伽辽金投影，这会导致与高阶解之间存在轻微偏差。本文基于分离式降阶算法，在物理和几何参数背景下求解湍流可压缩流动。在全阶层面，湍流采用涡粘性方法进行建模。鉴于存在多种不同的湍流模型来近似该附加粘性，本工作的目标之一是构建不受具体湍流模型选择的降阶模型。通过应用混合方法实现该目标：纳维-斯托克斯方程采用标准方式投影，而粘性场则通过数据驱动插值方法或经适当训练的神经网络进行评估。利用上述方法，可针对具有高雷诺数和高马赫数特征的全阶问题，预测出精确的流动解。