Sparsity-promoting reduced order modelling techniques for separated turbulent flows

这个博士项目的主要目标是开发一种新的模型稀疏化技术，该技术可以产生包含高雷诺数湍流关键特征的稀疏连接rom。在稀疏连接的ROM中，只保留动态相关的能量转移，因此可以显着降低与模拟相关的计算成本。研究的重点将是1)开发数据驱动的方法来解开稀疏性，使用完善的统计和机器学习技术，2)将这些方法与问题的潜在物理关联起来，3)对雷诺数，稀疏性和计算成本之间的相互作用进行广泛的参数调查。建模技术将在一个涉及代表性湍流分离流的测试案例中进行演示，该测试案例将在南安普顿大学的高性能计算设备IRIDIS上进行全分辨率数值模拟。

The main objective of this PhD project is to develop a novel model sparsification technique that produces sparsely-connected ROMs incorporating the key features of high Reynolds number turbulence. In a sparsely-connected ROM only the dynamically relevant energy transfers are retained, hence the computational cost associated to simulation can be significantly reduced. The focus of the research will be on 1) developing data-driven methods to unravel the sparsity, using well-established statistical and machine learning techniques, 2) correlate these methods to the underlying physics of the problem and 3) perform an extensive parametric investigation on the interaction between Reynolds number, sparsity and computational costs. The modelling technique will be demonstrated in a test case involving a representative turbulent separated flow, for which fully-resolved numerical simulations will be performed on IRIDIS, the high performance computing facility of the University of Southampton.