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

本研究计划的目标是发展一种高阶不连续伽辽金方法，用于紊流的大涡模拟。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，通常称为隐式LES建模。自由参数基于表面和体积积分的不同近似，以及使用有限体积方法的杂交，并针对子网格尺度上的效应建模进行了优化。这是由基于梯度的优化方法完成的，即使对敏感参数也保持鲁棒性和有效性。对于必要导数的计算应用伴随微积分，这是实现在一个自动化的方式使用算法微分。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竞争力在该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.