Large eddy simulations of turbulent thermal convection using renormalized viscosity and thermal diffusivity

TL;DR

This paper develops a subgrid-scale model using renormalized viscosity and thermal diffusivity for large eddy simulation of turbulent thermal convection, effectively capturing high Rayleigh number behaviors with good agreement to DNS results.

Contribution

The paper introduces a novel LES subgrid-scale model based on renormalized parameters, enabling accurate simulation of turbulent thermal convection at very high Rayleigh numbers.

Findings

LES results agree well with DNS for kinetic energy and entropy evolution.

The model accurately reproduces spectra and fluxes of velocity and temperature.

Successfully simulates convection at Rayleigh number 10^18.

Abstract

In this paper we employ renormalized viscosity and thermal diffusivity to construct a subgrid-scale model for large eddy simulation (LES) of turbulent thermal convection. For LES, we add $\nu_\mathrm{ren} \propto \Pi_u^{1/3} (\pi/\Delta)^{-1/3}$ to the kinematic viscosity; here $\Pi_u$ is the turbulent kinetic energy flux, and $\Delta$ is the grid spacing. In our model, the turbulent Prandtl number is unity. We performed LES of turbulent thermal convection on a $128^3$ grid and compare the results with direct numerical simulation (DNS) on a $512^3$ grid. There is a good agreement between the LES and DNS results on the evolution of kinetic energy and entropy, spectra and fluxes of velocity and temperature fields, and the isosurfaces of temperature. We also show the capability of our LES to simulate thermal convection at very high Rayleigh numbers and exhibit some results for $\mathrm{Ra=10^{18}}$.