Variational multiscale method in large eddy simulations of turbulent flows for fluid-structure interaction

对于许多具有工程意义的流固耦合问题来说，考虑湍流效应是绝对必要的。如今，大涡模拟似乎是处理这些湍流效应的唯一合理的方法，适用于一大类问题，而且是在计算上可以接受的方式。一种新开发的三层有限元方法将被采用和升级，作为本项目将开发和研究的变分多尺度方法/大涡模拟方法的基础。这三个级别分别代表已分辨的粗尺度、已分辨的小尺度和未分辨的小尺度，其中第一个水平用标准有限元近似，第二个水平用剩余自由气泡的方式分解，第三个水平用来确定亚格子的粘性。在深入研究这一基本方法之后，该项目的主要重点将是小尺度方程的全局-局部策略、尺度空间和次网格模型的分析和适应以及将这一多尺度策略嵌入整体求解方法。第二个项目期将集中于扩展到依赖于时间的区域，并纳入到我们的三场流体结构相互作用解算器中。这将是处理最具工程意义的问题类的重要一步，例如风激励的薄壁结构的空气动力学问题，柔性体的涡流脱落和一些生物力学问题。

The inclusion of turbulence effects is absolutely mandatory for many fluid-structure-interaction problems of engineering interest. Nowadays Large Eddy Simulation seems to be the only reasonable approach for treating these turbulence effects for a wide class of problems and in a computationally acceptable way. A newly developed three-level finite element method will be employed and upgraded to serve as basement for the Variational Multiscale Method/Large Eddy Simulation approach that will be developed and studied within this project. The three levels stand for the resolved coarse scales, the resolved small scales and the unresolved small scales, respectively, where the first level is approximated in a standard FE sense, the second level is resolved in a residual free bubble manner and the third level is used for the determination of a subgrid viscosity. After intensive studies of this basic approach the main focus of the project will be on global-local strategies for the small scale equations, the analysis and adaption of scale spaces and subgrid-models and on the embedding of this multiscale strategy in overall solution approaches. The second project period will concentrate on the extension to time-dependent domains and on the incorporation into our three-field fluid structure interaction solver. This will be a major step in the treatment of problem classes of utmost engineering interest, like aerodynamical problems of wind-excited thin-walled structures, vortex shedding of flexible bodies and some biomechanical problems.