Efficient representation of turbulent flows using data-enriched finite elements

Efficient modal decomposition of high-dimensional turbulent flow data is an important first step for data reduction, analysis, and low-dimensional predictive modeling. The conventional modal decomposition techniques, such as proper orthogonal and dynamic mode decompositions, aim to represent the system response using spatially global basis vectors that span a broad spatial domain. A significant challenge facing approaches based on global domain decomposition is the rapid increase in both the amount of training data and the number of modes that must be retained for an accurate representation of convection dominated turbulent flows. An alternative generalized finite element (GFEM) based approach is explored for efficient representation of high-dimensional fluid flow data. Here, the standard finite element interpolation method is enriched with numerical functions that are learned from a small amount of high-fidelity training data over spatially localized subdomains. The GFEM approach is demonstrated on a 3D flow past a cylinder at Reynolds number of 100 000 and flows inside a 2D lid-driven cavity over a range of Reynolds numbers. Compared with a global proper orthogonal decomposition, the GFEM-based approach increases efficiency in reconstructing the datasets while also substantially reducing the amounts of training data.