Implicit subgrid modeling of large eddy simulations with gradient-based optimization methods

该研究方案的目标是发展一种用于湍流大涡模拟的高阶间断Galerkin方法。因此，引入了自由过程参数，使得近似误差取代了子网格建模的作用，通常被称为隐式大涡模拟。自由参数基于表面积分和体积积分的不同近似，以及使用有限体积方法的杂交，并针对亚网格尺度上的效果建模进行了优化。这是通过基于梯度的优化方法来实现的，即使对于敏感的参数，这些方法也保持健壮和高效。为了计算必要的导数，应用了伴随微积分，它是用算法微分以自动的方式实现的。斯图加特和凯泽斯劳滕两个工作组在开发高分辨率方法和基于伴随的优化方法方面的核心能力在这个项目中得到了完美的结合。

The goal of this research proposal is the development of a high order discontinuous Galerkin method for large eddy simulations of turbulent flows. Therefore free process parameters are introduced such that the approximation error takes over the role of subgrid modeling, usually referred to as implicit LES modeling. The free parameters are based on different approximations of surface and volume integrals, as well as a hybridization using a finite volume approach and are optimized with respect to the modeling of effects on a subgrid-scale. This is done by gradient based optimization methods, which remain robust and efficient even for sensitive parameters. For the calculation of the necessary derivatives adjoint calculus is applied, which is implemented in an automated manner using algorithmic differentiation. The core competencies of the two working groups in Stuttgart and Kaiserslautern in the development of high-resolution methods and adjoint-based optimization methods are combined in this project perfectly.