Machine Learning-Assisted Modeling of Pressure Hessian Tensor

Velocity gradient dynamics play a pivotal role in understanding various nonlinear phenomena in turbulent flows. In the evolution of velocity gradient dynamics, the pressure Hessian and the viscous Laplacian are two mathematically unclosed terms which need separate modeling. The current study models the pressure Hessian term using the tensor basis neural network (TBNN). The network is trained on direct numerical simulation (DNS) data of stationary incompressible turbulence conditioned on local flow topologies. We compare the topology-based TBNN model performance with the DNS results as well as with the unconditioned (raw) TBNN model. The model results are evaluated in terms of the strain rate and the pressure Hessian eigenvector alignments. The model captures some of the essential alignment features of the DNS results.