Implicit LES of high Mach and high Reynolds number compressible turbulent flows enhanced by multidimensional flow field information using optimized flux functions and targeted reconstruction procedures due to machine-learned nonlinear neural operators

高马赫数和高雷诺数可压缩湍流的隐式 LES，通过多维流场信息增强，使用优化的通量函数和机器学习非线性神经算子的目标重建程序

• 批准号: 525796191
• 负责人: Professor Dr.-Ing. Nikolaus Andreas Adams
• 金额: --
• 依托单位: Lehrstuhl für Aerodynamik und Strömungsmechanik
• 依托单位国家: 德国
• 项目类别: Priority Programmes
• 资助国家: 德国
• 项目状态: 未结题
• 来源: https://gepris.dfg.de/gepris/projekt/525796191?language=en
• 关键词: Implicit; LES; Mach; Reynolds; number

Within the scope of the research project, novel approaches for the implicit large eddy simulation of compressible gas flows at high Reynolds numbers are developed. The newly developed automatically differentiable simulation and optimization method JAX-Fluids based on a conservative finite volume method forms the basis for the execution of the project. This package makes it possible to make known and established methods for state reconstruction at the interface and for the approximate solution of the resulting Riemann problem much more flexible while complying with basic mathematical requirements, and to optimize them specifically for physically based characteristics. Three main components are envisaged for this purpose: 1) The flow field is locally analyzed and characterized in three dimensions. A previously trained Convolutional Neural Network evaluates the three-dimensional properties of the local flow field (shear, volume change, smoothness, anisotropy) and passes this information to the next two components. 2) The reconstruction procedure for calculating the states at the cell interface will be based on a set of Harten-type polynomials, which, in contrast to classical methods, will not be weighted by algebraic functions but will be replaced by a neural network specially trained for flow-physical processes. Successful approaches to implicit large eddy simulation use inherent properties of different discretization methods to implicitly obtain the SGS terms that would otherwise have to be explicitly determined in order to simultaneously achieve highest precision on shock waves as well as on turbulence characteristics. 3) Established numerical flux functions, originally developed for the simulation of frictionless compressible flows, often allow a high simulation quality and shock waves, but are often much too dissipative for the representation of turbulent structures. In addition, Galilean invariance can usually not be guaranteed. In the context of this project, a neural network is used again, which combines the convex combination of classical flux functions such as HLLC and significantly less dissipative approaches such as ALDM, which are particularly suitable for the respective local flow field. The peculiarity, originality and novelty in the proposed project is that the training phase of the networks is performed by automatic differentiation of the entire flow solver. Here, the objective function required for optimization is a combination of point-wise errors versus low-pass filtered reference data from DNS and high-resolution LES, as well as their spectral characteristics. The goal of the project is to obtain results of comparable precision to state-of-the-art methods with significantly reduced spatial and temporal resolution and thus significantly reduced numerical effort.

在研究项目范围内，开发了高雷诺数下可压缩气体流动的隐式大涡模拟的新方法。新开发的基于保守有限体积法的自动微分模拟和优化方法jax - fluid构成了项目实施的基础。该软件包使得已知和已建立的界面状态重建方法以及由此产生的黎曼问题的近似解在符合基本数学要求的同时更加灵活，并且可以针对基于物理的特征进行优化。为此设想了三个主要组成部分：1)对流场进行局部分析和三维表征。预先训练的卷积神经网络评估局部流场的三维特性（剪切、体积变化、平滑度、各向异性），并将这些信息传递给接下来的两个组件。2)计算细胞界面状态的重建过程将基于一组harten型多项式，与经典方法不同的是，该多项式不会被代数函数加权，而是由专门针对流物理过程训练的神经网络代替。隐式大涡模拟的成功方法利用不同离散化方法的固有特性来隐式地获得SGS项，否则必须显式地确定这些项，以便同时实现对激波和湍流特性的最高精度。3)建立的数值通量函数，最初是为模拟无摩擦可压缩流动而开发的，通常允许高模拟质量和激波，但对于湍流结构的表示通常过于耗散。此外，通常不能保证伽利略不变性。在本项目的背景下，再次使用了神经网络，它结合了经典通量函数（如HLLC）的凸组合和耗散较小的方法（如ALDM），特别适用于各自的局部流场。该方案的独特性、独创性和新颖性在于网络的训练阶段是通过整个流求解器的自动微分来完成的。这里，优化所需的目标函数是点向误差与来自DNS和高分辨率LES的低通滤波参考数据的组合，以及它们的光谱特性。该项目的目标是获得与最先进的方法相当精度的结果，大大降低了空间和时间分辨率，从而大大减少了数值工作。