A consistent approach for the coupling of radiation and hydrodynamics at low Mach number

We present a consistent numerical model for coupling radiation to hydrodynamics at low Mach number. The hydrodynamical model is based on a low-Mach asymptotic in the compressible flow that removes acoustic wave propagation while retaining the compressibility effects resulting from combustion. Radiative transfer is modelled by the M1 entropy equations that can be viewed as a moment method. The radiation model possesses the capability to accurately approximate solution of radiative transfer at low computational cost while retaining the main physical properties of radiative energy. Consistent numerical approaches are developed for space and time discretizations in both hydrodynamics and radiation. A modified projection method is used for hydrodynamics, whereas an HLL-type discretization is implemented for radiation transport. The combined methods permit time steps that are controlled by the advective time scales resulting in a substantial improvement in computational efficiency compared to a compressible formulation. Numerical results are presented for the natural convection in a squared cavity with large temperature difference and also for a diffusion methane/air flame with four-step reduced chemical reactions in non-gray participating media. The present approach has been found to be feasible and satisfactory.