Data-driven artificial viscosity closures for projection-based reduced order modeling of incompressible fluid flows*

Advancements in computational hardware and physical simulation techniques have pushed the envelope of the complexity of fluid physics that can be modeled with adequate accuracy. However, these high-fidelity simulations are expensive for multi-query applications, real-time simulation and dynamics forecasting. In such situations, reduced order models (ROMs) are an attractive alternative as they can simulate engineering systems at a lower computational overhead without a significant loss in accuracy. Projection-based ROMs rely on offline-online model decomposition, where the data-based energetic spatial basis obtained from data is used in the expensive offline stage to obtain equations of reduced states that evolve in time during the inexpensive online stage.

The dynamic evolution of a large number of these reduced states in the online stage can be expensive. In contrast, the accuracy significantly decreases if only a few reduced states are considered and the interactions of the unresolved states with the resolved states are unaccounted. Therefore, it is essential to model these interactions between resolved and unresolved states. In this talk, we propose three closure model forms based on global, modal and tensor artificial viscosity approximation to account for these interactions. The unknown model parameters in these model forms are determined using two calibration techniques: least squares minimization of error in energy approximation and closure term approximation. This talk demonstrates that an appropriate selection of solution methods and data-driven artificial viscosity closure models is essential for consistently accurate dynamics forecasting of incompressible fluid flows.