Stability of 2D two-phase reactive flows

Abstract
Many problems of heterogeneous explosions incorporating convective flows, ignition, combustion, detonation, phase transition, etc. are mathematically formulated in terms of differ- ential conservation equations of mass, momentum and energy for a two-phase flow. In view of it, well-posedness of the corresponding Cauchy problem becomes an important issue. Well-posedness is treated as the capability of a mathematical model to avoid amplification of perturbations of ar- bitrarily high frequency. The problem of well-posedness is known to be closely connected with flow stability and to determine the correctness of computational studies of the mentioned phenomena. Theoretical analysis of well-posedness of two-phase flow models is presented. It is shown that 2D and 1D formulations differ essentially from each other in terms of well-posedness conditions. The approach making the two-phase problem unconditionally well-posed have been suggested.