Nonlinear closure modeling in reduced order models for turbulent flows: a dynamical system approach

Reduced-order models (ROM) of structurally dominated fluid flows have significant applications in science and engineering, such as design, control, and optimization. Proper-orthogonal decomposition (POD) modes are often computed from the flow field data and is one of the most successful ROM strategies. However, its application to turbulent flows remains a challenging task. For laminar flows, higher modes are often discarded in the development of ROM to obtain the computational advantage over the full-order simulation. Although these higher modes contain relatively lower energy than the first few modes, they are responsible for viscous dissipation. For turbulent flows, the viscous effects are modeled in a ROM framework through linear and nonlinear closure modeling techniques. This study presents a computationally efficient nonlinear closure model which is based on a dynamical system approach. We consider 3D flow field around a cylinder at Reynolds number of 1000 with turbulent wake. We compute the POD modes and develop a conventional ROM. We then add a closure term analogous to the large-eddy simulation approach. The key contribution is the application of proposed closure for turbulent flows. Numerical results demonstrate that the proposed model is computationally efficient as compared to other nonlinear closure models while maintaining the same order of accuracy.