A boundary condition capturing method for incompressible flame discontinuities

In this paper, we propose a new numerical method for treating two-phase inc ompressible flow where one phase is being converted into the other, e.g., t he vaporization of liquid water. We consider this numerical method in the c ontext of treating discontinuously thin flame fronts for incompressible flo w. 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 c apturing technology developed in Liu et al. (2000, J. Comput. Phys. 154, 15 ) for the variable coefficient Poisson equation and in Kang et al. (in pres s J. Comput. Phys.) for multiphase incompressible flow. Our new numerical m ethod admits a sharp interface representation similar to the method propose d in Helenbrook et al. (1999, J. Comput. Phys. 148, 366). Since the interfa ce boundary conditions are handled in a simple and straightforward fashion, the code is very robust, e.g. no special treatment is required to treat th e merging of flame fronts. The method is presented in three spatial dimensi ons, with numerical examples in one, two, and three spatial dimensions. (C) 2001 Academic Press.