"A modification of the CABARET scheme for numerical simulation of one-dimensional detonation flows using a one-stage irreversible model of chemical kinetics"
Danilin A.V., Solovjev A.V., and Zaitsev A.M.

An algorithm for numerical simulation of one-dimensional detonation using a one-stage irreversible model of chemical kinetics is proposed. The discretization of the convective parts of governing equations is made in accordance with the balance-characteristic CABARET (Compact Accurately Boundary Adjusting-REsolution Technique) approach. The approximation of source terms is performed implicitly without splitting into physical processes with a regulated order of approximation. It is shown that the numerically obtained Chapman-Jouget detonation parameters are in exact agreement with the analytical solution. It is also shown that, in the case of unstable detonation, the numerical results are dependent on the order of approximation chosen for the right-hand sides of the governing equations.

Keywords: one-velocity multicomponent medium, systems of hyperbolic equations, CABARET scheme, computational fluid dynamics (CFD), conservative methods, detonation, Arrhenius reaction.

  • Danilin A.V. – Nuclear Safety Institute, Russian Academy of Sciences; ulitsa Bol’shaya Tul’skaya 52, Moscow, 115191, Russia; Junior Scientist, e-mail: adanilin@ibrae.ac.ru
  • Solovjev A.V. – Nuclear Safety Institute, Russian Academy of Sciences; ulitsa Bol’shaya Tul’skaya 52, Moscow, 115191, Russia; Ph.D., Leading Scientist, e-mail: solovjev@ibrae.ac.ru
  • Zaitsev A.M. – Nuclear Safety Institute, Russian Academy of Sciences; ulitsa Bol’shaya Tul’skaya 52, Moscow, 115191, Russia; Junior Scientist, e-mail: azai@ibrae.ac.ru