Physics Guided Neural Networks for Spatio-temporal Super-resolution of Turbulent Flows*

Direct numerical simulation (DNS) of turbulent flows is computationally expensive and is not practical for simulating flows at high Reynolds numbers. Low-resolution large eddy simulation (LES) is a pragmatic alternative, but its success depends on modeling of the small scale flow dynamics. Reconstructing DNS from low-resolution LES is critical for many scientific and engineering disciplines, but it poses many challenges to existing super-resolution methods due to the complexity of turbulent flows and computational cost of generating frequent LES data. In this work, we propose a physics-guided neural network for reconstructing frequent DNS from sparse LES data by enhancing its spatial resolution and temporal frequency. Our proposed method consists of a partial differential equation (PDE)-based recurrent unit for capturing underlying temporal processes and a physics-guided super-resolution model that incorporates additional physical constraints. We demonstrate the effectiveness of both components in reconstructing the data generated by simulating the Taylor-Green Vortex sparse LES data. Moreover, we show that the proposed recurrent unit can preserve the physical characteristics of turbulent flows by leveraging the physical relationships in the Navier-Stokes equation.