USING VARIATIONAL MECHANIC PRINCIPLES FOR CONSTRUCTION OF TIME-DISCRETE DIFFERENCE MODELS IN GAS DYNAMICS. PT.5. PULSE AND PULSE MOMENTUM CONSERVATION LAWS IN DIFFERENCE SCHEMES WITH HOLONOMIC BOUNDS

Yu.A. Bondarenko
VANT. Ser.: Mat. Mod. Fiz. Proc 1992. Вып.1. С. 21-27.

      Finite-difference gasdynamic shemes ("cross" type and implicit "weighted" schemes) on Lagrangian meshes are considered.
      If the cell volumes and holonomic bounds are Invariant with respect to space translations and rotations, the pulse arid pulse momentum conservation laws are shown to be satisfied for diffe-rence schemes implemented with a sequential variational method using a discrete time approximation of the Hamilton-Ostrogradsky action functional. Several examples show that using time approximation which is not consistent with the principle of least action results in that pulse momentum conservation law becomes no longer valid while the same invariance conditions hold.

      Differential/difference schemes and several finite-difference gas- dynamic scheme types with a kinetic energy operator depending on mesh node coordinates are examined. If cell values, holonomlc bounds and kinetic energy are invariant with respect to space translations and rotations then pulse or pulse momentum conservation laws are satisfied, respectively, for difference schemes developed with a sequential variational method based on time approximation of the Hamilton-Ostrogradsky action functional.