A heterogeneous multiscale method for stiff combustion chemistry integration in reactive flows

The concept of heterogeneous multiscale method (HMM) is applied into combustion chemistry integration in reactive flows in this study. It adopts a macro solver to integrate the slow variables with global time steps and a micro solver to integrate the fast variables with smaller inner time steps. Explicit or implicit schemes with different orders of accuracy could be applied in the macro and micro solvers. In this study, we formulated HMM with a first-order Euler forward scheme in the micro solver and a second-order trapezoidal rule in the macro solver. An adaptive time step method was proposed to better evaluate a proper time step and control the error in this HMM. This formulation of HMM with the adaptive time step method has been implemented and tested in homogeneous constant volume auto-ignition in hydrogen, methane and butane mixture under various initial temperatures, pressures and equivalence ratios. The speed-up factor of 100-700 has been achieved compared with the implicit solver DASAC. In addition, the numerical accuracy and stability of this HMM formulation have been discussed. It was also applied into multi-dimensional Reynolds-averaged Navier-Stokes (RANS) engine simulations and good efficiency and accuracy was accomplished. In order to better optimize its efficiency performance in multi-dimensional reactive flow simulations, a hybrid scheme with VODE and HMM was proposed and tested in non-homogeneous charged engine simulations. In sum, the concept of HMM in stiff combustion chemistry integration is numerically stable, accurate and efficient.