Data-Driven Closure Modelling of the Navier-Stokes Momentum Equations

Abstract

An approach to data-driven closure modelling in the framework of variational multiscale method for large eddy simulation is presented. A turbulent channel flow at the friction Reynolds number of 180 is used as a case study. Challenges in the modelling linked to the continuity closure terms force the scope of the study to be narrowed to only momentum Navier-Stokes equations. By using integrated forms of the resolved flow solution to train a multi-layer perceptron closure model, high a priori correlations with true closure terms can be achieved. Validation of the data-driven closure models a posteriori shows that the models are suitable for the computation of the velocity field, but fail to obtain a physical pressure solution. Accumulation of the model error leads to a decay of the kinetic energy of the mean flow, while the resolved turbulent fluctuations become excessively energized. Novel techniques such as data augmentation, mini-batch sum loss and filtering of the closure terms are presented and evaluated via large eddy simulations.