J. Phys. IV France 12 (2002) Pr7-437
Stability of 2D two-phase reactive flowsYu.B. Radvogin1, V.S. Posvyanskii2 and S.M. Frolov2
1 V.M. Keldysh Institute forApplied Mathematics, Moscow, Russia
2 N.N. Semenov Institute of Chemical Physics, Moscow, Russia
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.
© EDP Sciences 2002