APPLICATION OF VARIATIONAL PRINCIPLES OF MECHANICS TO DEVELOPING TIME-DISCRETE DIFFERENCE GAS DYNAMICS MODELS. 1. DESCRIPTION OF THE METHOD ON SIMPLE EXAMPLES

Yu. A. Bondarenko
VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki 1985. Вып.2. С. 68-75.

      A method of constructing simultaneously time - and space-discrete difference1 schemes is described for a set of gas dynamics equations in Lagragian variables. The method is based on the use the Hami1ton-Ostro-gradski principle, the time- and space-integrals of the Lagrangian function in action functional being replaced with appropriate quadrature formulas. The described method is a natural extension of variational method constructing differential-difference schemes for gas dynamics, developed in papers by Golovizin V. M., Samarski A. A, and Favorski A. P., and, in contrast with them, allows to construct time-difference approximations directly.