"A higher-order difference scheme of the Cabaret class for solving the transport equation"
Solovjev A.V. and Danilin A.V.

A new difference scheme of the Cabaret class with a higher order of accuracy for solving the scalar transport equation is proposed. The order of approximation of this difference scheme is equal to four. The balance-characteristic representation of the scheme is constructed and the dispersion properties are given. For the proposed difference scheme, a number of examples to solve the transport equation for smooth and discontinuous profiles are considered in comparison with the classical Cabaret scheme.

Keywords: Cabaret scheme, transport equation, higher order approximation, accuracy.

  • 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
  • Danilin A.V. – Nuclear Safety Institute, Russian Academy of Sciences; ulitsa Bol’shaya Tul’skaya 52, Moscow, 115191, Russia; Junior Scientist, e-mail: bass-4@yandex.ru