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MECHANICS VARIATIONAL PRINCIPLES APPLICATION TO CONSTRUCT TIME DISCRETE GAS DYNAMICS DIFFERENCE MODELS. 7. CONSERVATION OF PHASE VOLUME AND CANONICITY IN FINITE-DIFFERENCE SCHEMES OF "CROSS"-TYPE

Yu. A. Bondarenko
VANT. Ser.: Mat. Mod. Fiz. Proc 2011. Вып.1. С. 3-16.

Conservation of phase volume and canonicity (hamiltonicity) islb proved for finite-difference schemes of Lagrangian gas dynamics constructed with variational stepwise method for which time and space discrete statement of Hamilton-Ostrogradsky principle of least action is used. Canonicity conservation is valid in certain cases only for complex "implicit" impulses.

Keywords: Lagrangian gas dynamics, principle of least action, variational difference schemes, difference schemes of "cross"-type, phase volume, canonicity.
ON "STAGGERED ORDER EFFECT" IN CERTAIN DIFFERENCE SCHEMES FOR 2D AND 3D HEAT CONDUCTIVITY

Yu. A. Bondarenko, A. A. Golubev, A. A. Gorbunov, A. O. Naumov, A. I. Panov
VANT. Ser.: Mat. Mod. Fiz. Proc 2011. Вып.1. С. 3-16.

Shown here is the staggered order effect producing capacity in certain schemes used for 2D and 3D heat conductivity computations. It takes place when temperature difference gradient derived from formulas similar to pressure gradient computational method in Lagrangian difference schemes, is used for approximation of flows across the edges. In point source problems, the main interaction in square and cube grid is diagonal. Described here is the way to avoid the staggered order effect.

Keywords: radiative heat conductivity, temperature difference gradient, regular and irregular grids, test computations.







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