Abstracts

Siberian participants

About some family difference schemes gaseous dunamics with positively determined Matrix

V.V. Zharovtzev

The approach permitting for the non-stationary equations of gaseous dynamics in approximation the Euler on a minimum grid mask to build explicit difference networks such as predictor - corrector - an equalizer with positive definite matrixes (the monotone schemes) is stated. Property of a monotonicity, as well as the stability conditions, are erected for the relevant linear analogs of difference equations.

At a stage predictor in the differential equations recorded in undivergent to the shape, each function at derivative on spatial coordinate is artificial it is represented as binomial. The difference analogues of the "elementary" differential equations obtained as a result of application of a procedure of splitting, are recorded with engaging of Lax approximating with the pitch on time (parameter of the schemes). The required difference equations used at the first stage, are the total of the relevant "elementary" difference analogues. For the one-dimensional, two-dimensional and three-dimensional equations of gaseous dynamics the multiparameter sets of the circuits of the first order of approximating with positive definite matrixes are chosen. The approximating viscosity of the constructed difference equations is sufficient for open calculation of noncontinuum flows of gas. Some constructed one-dimensional circuits were tested on such currents.

Note. Abstracts are published in author's edition

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