Computational Mathematics and Mathematical Physics

, Volume 59, Issue 9, pp 1528–1541 | Cite as

Numerical Modeling of Wave Processes Accompanying Combustion of Inhomogeneously Distributed Composite Propellant

  • I. S. MenshovEmail author
  • M. Yu. NemtsevEmail author
  • I. V. SemenovEmail author


A mathematical model and a numerical method are proposed for studying the interior ballistic process related to combustion of inhomogeneously distributed propellant in the two-dimensional axisymmetric approximation. The gas–propellant mixture is modeled by a two-phase nonequilibrium heterogeneous medium consisting of a multicomponent gas phase of combustion products and a polydisperse solid phase of propellant granules. The mathematical model of nonequilibrium two-phase flow is based on the nonconservative Euler equations. A Godunov-type scheme with an approximate Riemann solver is developed for their solution. The propellant combustion is considered taking into account the motion of the projectile, which is modelled using the free-boundary method. Results are represented concerning the origin and evolution of the interior ballistic wave process proceeding during the combustion of an inhomogeneously distributed propellant charge and the motion of the projectile. A comparative analysis with the case of static (nonmoving) propellant is carried out.


two-phase nonequilibrium heterogeneous mixture interior ballistics combustion of granular propellant 



The authors are grateful to V.V. Chernov and A.K. Abdullin (JSC Central Research Institute Burevestnik, Nizhny Novgorod) for the provided experimental data and discussion of the results of this work. The computations were executed on the MVS-10P multiprocessor computer system at the Joint Supercomputer Center of the Russian Academy of Sciences.


This study was supported in part by the Russian Foundation for Basic Research, project no. 18-01-00921a. This work was carried out in part under the state task of the Scientific Research Institute for System Analysis of the Russian Academy of Sciences (basic scientific research GP 14), subject no. 0065-2019-0005 “Mathematical Modeling of Dynamic Processes in Deformable and Reacting Media on Multiprocessor Computer Systems” (project no. AAAA-A19-119011590092-6).


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Copyright information

© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.Scientific Research Institute for System Analysis, Russian Academy of SciencesMoscowRussia
  2. 2.Keldysh Institute of Applied Mathematics, Russian Academy of SciencesMoscowRussia
  3. 3.Institute for Computer Aided Design, Russian Academy of SciencesMoscowRussia

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