A compressible solver for the laminar–turbulent transition in natural convection with high temperature differences using implicit large eddy simulation

The transition induced by the natural convection with high temperature differences can be easily observed in many engineering applications. The compressible solver has to be taken into consideration because the usual way of using the incompressible solver with Boussinesq approximation is only available within the temperature difference of 30 K. However, speeds in natural convection are always several orders of magnitude lower than the speed in compressible regions. A modified compressible solver which can deal with the buoyancy-induced turbulence is proposed here. In this solver, an all speed preconditioned Roe (APRoe) is adopted to appropriately treat flows at extremely low speed regions. And then, a reconstruction method for the MUSCL scheme at low Mach numbers (M5LM) is applied to attenuate the dissipation. The numerical dissipation of the compressible solver is utilized as a subgrid scale (SGS) model for the implicit large eddy simulation (LES). Based on qualitative agreement with direct numerical simulation and considering the capability of numerically predicting a -3 decay law for the energy transfer induced by the natural convection in the temporal power spectrum of the temperature fluctuation, this solver is potentially a good candidate for laminar–turbulent transition in natural convection.