APPLICATION OF VARIATIONAL PRINCIPLES OF MECHANIES TO DEVELOPING TIME-DISCRETE DIFFERENCE GAS DYNAMICS MODELS. 2. HOLONOMIC BONDS, BOUNDARY CONDITIONS, AND STABILITY OF REST STATE IN "KREST"-TYPE DIFFERENCE SCHEMES

Yu. A. Bondarenko, A. M. Stenin
VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki 1986. Вып.1. С. 14-26.

      Development of the variational method generating difference schemes for a set of gas dynamics equations in Lagrangian variables is described which is based on time-discrete approximation of action functional and using Hami1ton-Ostrogradski principle. On an example of "KREST"-type difference schemes ways of accounting holonomic bonds are described which are used for approximation of boundary conditions, when the gas curvilinear boundary is given. It is shown how the virtual work principle should be used, when pressure at boundary is given. The scheme is constructed with allowance made for surface forces. Sufficient stability conditions are obtained on arbitrary Lagrangian meshes of general tyre. The coordinated introduction of holonomic bonds into the scheme is shown not to deteriorate stability conditions.