APPLICATION OF VARIATIONAL PRINCIPLES OF MECHANICS TO DEVELOPING TIME-DISCRETE DIFFERENCE GAS DYNAMICS MODELS. 3. NONUNIFORM DIFFERENCE SCHEMES WITH VARIOUS TIME-STEPS IN NEIGHBOURING CELLS

Yu. A. Bondarenko
VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki 1987. Вып.2. С. 3-10.

      Using finite-dimensional approximation of the Hami1ton-Ostrogradski functional on space-time irregular difference meshes the conservative variational difference schemes are derived allowing calculation of gas dynamics problems on arbitrary Lagrangian meshes with neighbouring-cell time steps which differ twice from one another. In subregions of the same time-steps in all the cells the derived difference schemes are equivalent to variational difference schemes of the "KREST" type. The numerical test results indicate that with the fixed neighbouring cell time-step ratio the additional error due to nonuniformity of the difference schemes proposed is small as compared to approximation errors of the standard difference scheme "KREST".