J. Phys. IV France
Volume 12, Numéro 7, August 2002
Page(s) 437 - 444

J. Phys. IV France
12 (2002) Pr7-437
DOI: 10.1051/jp4:20020313

Stability of 2D two-phase reactive flows

Yu.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.

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