A modification of the CABARET scheme for numerical simulation of one-dimensional detonation flows using a one-stage irreversible model of chemical kinetics


  • A.V. Danilin Nuclear Safety Institute (IBRAE) of RAS https://orcid.org/0000-0001-7349-0600
  • A.V. Solovjev Nuclear Safety Institute (IBRAE) of RAS
  • A.M. Zaitsev Nuclear Safety Institute (IBRAE) of RAS




iterative processes, Newton’s method, logarithmic derivative, continuous functions defined on a segment, higher order methods, interval of convergence, transcendental equations


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.

Author Biographies

A.V. Danilin

A.V. Solovjev

A.M. Zaitsev


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How to Cite

Данилин А.В., Соловьев А.В., Зайцев А.М. A Modification of the CABARET Scheme for Numerical Simulation of One-Dimensional Detonation Flows Using a One-Stage Irreversible Model of Chemical Kinetics // Numerical methods and programming. 2017. 18. 1-10. doi 10.26089/NumMet.v18r101



Section 1. Numerical methods and applications