A directional ghost-cell immersed boundary method for low Mach number reacting flows with interphase heat and mass transfer

• General Robin (Neumann) BC are accurately imposed and satisfied. • Neither polynomial assumptions or complex interpolations are required. • Low Mach number variable-density flows are considered. • Reaction-induced interfacial phenomena can be accurately resolved. • Second-order accuracy is preserved for all the implementations. This paper presents a directional ghost-cell immersed boundary method for low Mach number reacting flows with general boundary conditions, extending the approach described in Chi et al. (2020) [17] . The method employs locally directional schemes for ghost value reconstruction and utilization along each discretization direction. In this manner, the boundary condition can be naturally imposed on the boundary intersection point along each coordinate direction, allowing an easy and straightforward implementation of complex boundary conditions. Using Taylor series approximation of fluid points near the immersed boundary, the boundary variable and its gradient governed by arbitrary boundary condition can be implicitly involved, leading to a reliable polynomial extrapolation for the ghost values. In this way, Dirichlet, Neumann and Robin boundary conditions are implemented for general variables with formally second-order accuracy. For reacting gas-solid flow with surface reactions, the reaction-related coefficients in Robin boundary condition lead to a complex implementation in conventional IBM techniques, while the present directional framework leads to a straightforward algorithm while preserving accuracy. The proposed method has been checked by a series of test cases with different boundary conditions, including basic flow, heat and species transport, Stefan problem, and finally two practical applications involving heat and mass transfer. The local accuracy of all boundary conditions exhibits nearly second-order convergence, as expected. While only a single solid object is considered in this first work, the same method can be simply extended to multiple objects of arbitrary shape, leading to fully resolved simulation of reactive particle-laden flows.