Propagator-moments approximation for recurrence CFD: Application to species transport in turbulent flows

Abstract

Accurate, long-term simulations of turbulent flows pose a large challenge for standard CFD algorithms. Recurrence CFD (rCFD) provides a simple, data-assisted approximation for recurrent dynamics. We present the theoretical foundations of this approach in terms of propagator theory for passive transport processes and derive expressions for convective and diffusive contributions to large-step species transfer. We tested our new implementation on a double-sided, cuboid lid-driven cavity and compared various treatments of diffusion against detailed CFD calculations. Based on these insights, we applied the methodology to a down-scaled, industrial case of impurity transport in a steelmaking tundish at Reynolds number $Re=220,000$. We obtained results in mostly very good agreement with detached-eddy simulations at 1/2700 of their runtime, which made rCFD faster than real time.