"Using the Sharp scheme of higher-order accuracy for solving some nonlinear hyperbolic systems of equations"
Solovjev A.V. and Danilin A.V.

The Sharp difference scheme of higher-order accuracy developed previously for solving the scalar one-dimensional transport equation is extended to the shallow water nonlinear systems and to the systems of Euler equations using the balance-characteristic approach. For these systems, a number of test problems are solved to illustrate the features of the solutions obtained by the described difference scheme.

Keywords: Cabaret method, Sharp scheme, hyperbolic equations, high-accuracy schemes.

  • 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