Projection-based reduced order modeling and data-driven artificial viscosity closures for incompressible fluid flows

TL;DR

This paper advances reduced order modeling for incompressible fluid flows by integrating an incremental pressure correction scheme with data-driven artificial viscosity closures, improving accuracy and efficiency in online dynamic evolution.

Contribution

It introduces the use of the incremental pressure correction scheme in reduced order models and compares three artificial viscosity closure models for better accuracy.

Findings

Incremental pressure correction scheme effectively models pressure and velocity evolution.

Artificial viscosity closures improve the interaction modeling between resolved and unresolved states.

Data-driven parameter calibration enhances model accuracy.

Abstract

Projection-based reduced order models rely on offline-online model decomposition, where the data-based energetic spatial basis is used in the expensive offline stage to obtain equations of reduced states that evolve in time during the inexpensive online stage. The online stage requires a solution method for the dynamic evolution of the coupled system of pressure and velocity states for incompressible fluid flows. The first contribution of this article is to demonstrate the applicability of the incremental pressure correction scheme for the dynamic evolution of pressure and velocity states. The 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 while not accounting for the interactions between unresolved and resolved states. The second contribution of this article is to compare three closure model forms based on global, modal and tensor artificial viscosity approximation to account for these interactions. The unknown model parameters are determined using two calibration techniques: least squares minimization of error in energy approximation and closure term approximation. This article 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.