Examination of Well-Posedness of Multi-Fluid Model

In order to perform a reasonable numerical prediction of two -phase flow based on a multi-fluid model, it is necessary for us to understand whether the model constitutes a well-posed or ill-posed initial-value problem. Otherwise, we cannot take appropriate measures for numerical instability caused by ill-posedness. Hence, mathematical characteristics of several multiphase models such as a one-dimensional three-fluid model, a two-dimensional two-fluid model and a dispersed flow model were examined in the present study. For this purpose, the existing mathematical method for evaluating the well-posedness was reviewed in detail. It was pointed out by this review that the existing method is applicable to a model of incompressible multiphase flow as well as compressible multiphase flow even though the coefficient matrix of the incompressible model is singular. Then, the well-posedness of several multi-fluid models and dispersed flow models was clarified.