Computational Fluid Dynamics Laboratory
School of Mechanical and Aerospace Engineering, Oklahoma State University
We are developing advanced computational methods for nonlinear dynamical systems driven by multiscale and multiphysics processes. The systems studied in our lab range from engineering flows to geophysical flows with different levels of complexities. There is an emphasis on modeling and analysis of turbulent flows across a variety of spatial and temporal scales. Our current efforts are centered in the development of Hybrid Analysis and Modeling (HAM) approaches in LES and ROM frameworks. Integrating different ways of physics-based and machine learning/data-driven modeling approaches, we advocate hybrid modeling approaches for emerging digital twin technologies, and exploit our HAM framework that embraces flexibility to use most effective tools depending on the problem and its challenges.
Large Eddy Simulations
The goal of large eddy simulation, which is one of the most successful approaches for simulating turbulent flows, is to decompose the flow into large and small scales by convolving the flow with a spatial low-pass filter. This process results in a well-known closure problem due to the nonlinearity of the underlying governing equations. Currently, we are working on functional, structural and data-driven closure modeling ideas to take into account subgrid-scale effects in large eddy simulations. Closure modeling refers to the process of including the truncated scales (due to the limited numerical resolution & computational resources) into the resolved dynamics (the scales captured in our underlying numerical model) to account for the missing subgrid-scale physics, which is quite important if the underlying dynamical process is nonlinear with strong interactions between small and large scales.
Reduced Order Modeling
Reduced order models are extremely low-dimensional models that can decrease the computational cost of current computational models by orders of magnitude. Simplifying computational complexity of the underlying mathematical model, these models offer promises in settings, especially where the traditional methods require repeated model evaluations over a large range of parameter values. To develop such low dimensional models that are accurate in realistic problems, the closure problem needs to be solved, i.e., the effect of the discarded modes on the model dynamics needs to be modeled.
Closure modeling analogy between large eddy simulation (LES) and reduced order modeling (ROM).