A Boundary Condition Capturing Method for Incompressible Flame Discontinuities

In this paper, we propose a new numerical method for treating two-phase incompressible flow where one phase is being converted into the other, e.g., the vaporization of liquid water. We consider this numerical method in the context of treating discontinuously thin flame fronts for incompressible flow. This method was designed as an extension of the Ghost Fluid Method (1999, J. Comput. Phys.152, 457) and relies heavily on the boundary condition capturing technology developed in Liu et al. (2000, J. Comput. Phys.154, 15) for the variable coefficient Poisson equation and in Kang et al. (in press J. Comput. Phys.) for multiphase incompressible flow. Our new numerical method admits a sharp interface representation similar to the method proposed in Helenbrook et al. (1999, J. Comput. Phys.148, 366). Since the interface boundary conditions are handled in a simple and straightforward fashion, the code is very robust, e.g. no special treatment is required to treat the merging of flame fronts. The method is presented in three spatial dimensions, with numerical examples in one, two, and three spatial dimensions.