Comparing assimilation techniques for pressure and temperature fields in Rayleigh-Bénard convection

Abstract

We compare two methods to assimilate temperature and pressure fields based on given three-dimensional velocity fields of moderately turbulent Rayleigh-Bénard convection in a cubic geometry with system parameters Rayleigh and Prandtl number: Ra , Pr . The first method describes a direct solution of the problem using the fractional step of the associated Navier-Stokes equation. The second method uses a physically informed neural network approach that learns the associated temperature and pressure fields by minimizing the residual loss of the set of equations governing the flow. The ground truth temperature, pressure, and velocity fields originate from a direct numerical simulation.