A Projected Ghost Fluid Method for a mimetic approach for extreme contrast interfaces in multiphase flows

Abstract

In the context of a multimaterial domain, the GFM for the Laplacian operator is reformulated from an algebraic perspective, where operators are represented by matrices. From this perspective, a whole new level of analysis can be attained. Namely, conceiving mass, heat and momentum transfer applications, the discretization of both value and flow discontinuities is discussed, with particular emphasis on extreme contrast interfaces, such as those arising in liquid-vapor mixtures. Regarding ¿ow discontinuities, the GFM is shown to result in an o¿-image linear system of equations for the Poisson problem. In order to ¿x this issue, the Projected Ghost Fluid Method (PGFM) takes a global approach to the discretization strategy in order to correct the standard GFM and thus guarantee a consistent discretization. Apart from being mathematically neat and resulting in a compatible linear system of equations, the PGFM shows enhanced robustness in dealing with extreme contrast interfaces. A comparison study is presented for several coeffient ratios.