A path-conservative DG formulation for large-eddy simulations of reacting and multi-physics flows

The present study proposes a new DG formulation to address the numerical issues associated with the application of DG scheme to flow problems with complex thermodynamic models. Specifically, the proposed formulation solves an auxiliary pressure variable, of which the governing equation is derived based on the equation of state (EoS) and the consistent LES-filtering. As a result, the LES-resolved pressure is obtained by solving a time-dependent PDE, instead of inversion based directly on the EoS that introduces formulation inconsistency and large modeling errors in the context of LES. The proposed method is firstly validated by considering a set of homogeneous isotropic turbulence cases. The advantages of the proposed numerical treatment will be highlighted in the comparison between LES results obtained using both the new and classical EoS-based formulations. Finally, the capability of the proposed method will be demonstrated in the application to the simulation of a turbulent jet flame.