A unified modeling paradigm for turbulence, shock waves and boundary layers in computational compressible aerodynamics

可压缩流动的高精度计算机模拟需要可靠的湍流、激波和边界层模拟方法。现有的模拟方法在单独模拟每一种现象时都取得了很好的效果，但当湍流、激波和边界层同时发生时，它们会以一种不受欢迎的方式相互作用。例如，基于人工粘性的处理激波的数值方法往往会影响湍流模型，从而使模拟结果变得非物理的。该项目是基于这样一种假设，即综合考虑这三种现象的模拟方法可以显著提高湍流可压缩流动的模拟精度。在有限元方法的背景下，变分多尺度方法(VMS)是一种很有前途的湍流可压缩流动模拟工具，实际网格宽度不能分辨尖锐的内部层和边界层以及微小的湍流涡流。拟议项目的目的是开发一种基于VMS的湍流、激波和边界层统一建模方法，该方法基于物理模型的基本熵结构，并避免任何特殊机制。待开发的统一建模方法将被整合到基于高阶等距有限元的现代离散技术中。它在准确性和稳健性方面的性能以及它在工业应用中的潜力将通过飞机和涡轮机设计中具有挑战性的空气动力学模拟问题来研究和演示。

Highly accurate computer simulations of compressible flows require methods for the reliable modeling of turbulence, shock waves and boundary layers. Existing modeling approaches achieve good results when simulating every single phenomenon on its own, but they interact with each other in an undesirable manner when turbulence, shock waves and boundary layers occur together. For example, numerical methods based on artificial viscosity for treating shock waves often influence the turbulence model in such a way that the simulation result becomes unphysical. The proposed project is based on the hypothesis that an integrated approach that considers the modeling of all three phenomena together can significantly improve the simulation accuracy of turbulent compressible flows. In the context of the finite element method the variational multiscale method (VMS) constitutes a promising tool for the simulation of turbulent compressible flows, in which practical mesh widths cannot resolve sharp interior and boundary layers as well as tiny turbulent eddies. The aim of the proposed project is to develop a unified VMS-based modeling approach for turbulence, shock waves and boundary layers that is based on the underlying entropy structure of the physical model and avoids any ad hoc mechanisms. The unified modeling approach to be developed will be integrated into modern discretization techniques based on higher-order isogeometric finite element methods. Its performance in terms of accuracy and robustness and its potential for use in industrial applications will be investigated and demonstrated using challenging aerodynamic simulation problems from aircraft and turbine design.