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

点击翻译按钮获取中文摘要

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.