arXiv 2205.093962022-05physics.flu-dyncs.CEcs.NAmath.NA

湍流可压缩流动压力基求解器的分离降阶模型

A segregated reduced order model of a pressure-based solver for turbulent compressible flows

Matteo Zancanaro, Valentin Nkana Ngan, Giovanni Stabile, Gianluigi Rozza

AI总结：

本文提出一种针对湍流可压缩流动的分离降阶模型框架，通过混合方法投影Navier-Stokes方程并结合数据驱动或神经网络近似粘性场，实现对高雷诺数和高马赫数流场的准确预测。

摘要：

本文提供了一个针对使用有限体积方法离散化的湍流可压缩流动的降阶建模框架。这项工作的基本思想是构建一个降阶模型，能够提供与高保真流场高度准确的解。全阶解通常通过使用分离求解器（求解变量一个接一个地求解）获得，采用略微修改的守恒定律，以便它们可以被解耦，然后一次求解一个。相反，经典的降阶架构依赖于完整Navier-Stokes系统一次性投影的Galerkin投影，导致与高阶解存在轻微差异。本文依赖于分离降阶算法，在物理和几何参数背景下求解湍流和可压缩流动。在全阶层面，湍流使用涡粘性方法建模。由于存在多种不同的湍流模型用于近似这种补充粘性，本工作的目标之一是提供一个独立于此选择的降阶模型。该目标通过应用混合方法实现，其中Navier-Stokes方程以标准方式投影，而粘性场通过使用数据驱动的插值方法或通过评估适当训练的神经网络来近似。通过利用上述权宜之计，能够针对具有高雷诺数和高马赫数特征的全阶问题预测准确的解。

英文摘要：

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.

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