Tensor Networks for Solving the PDF/FDF Transport

 

The PDF-FDF methodologies have proven very effective for RANS-LES of chemically reactive turbulent flows.  Due to their inherent capabilities, the equations governing the transport of PDF/FDF are high dimensional. It is shown that  “tensor networks”  (TN) can deal with such a large dimensional transport in a very effective manner.  These networks are employed here to tackle the Fokker-Planck form of the PDF/FDF instead of the Langevin form as is typically done via Monte Carlo methodologies. Demonstrative simulations are conducted of a  chemically reactive flow, governed by a time-dependent five-dimensional  modelled Fokker-Planck equation.