Конференции ИВТ СО РАН

Abstracts

Approximation factorization methods and splitting methods are widely used for numerical solving of aero dynamical problems that are described by Navier-Stokes equations for compressible viscous heat-conducted gas. These methods allow to reduce solving of initial many-dimensional problems to sequence of their one-dimensional analogs or more simple problems. In this paper modifications of finite-differential schemes are considered. These schemes are based on splitting of initial operators on the physical process and spatial variables which allow them to keep properties of non-conditional stability and scalar solvability, satisfy property of minimal dissipation but demand less number of arithmetic operations for the node of a grid.

Basic properties of difference schemes have been tested on problems of arbitrary discontinuity one-dimensional flow and stationary gas flow in a channel with variable cross-section in a quasi one-dimensional approximation. The accuracy estimations of solution and optimal time step have been presented using stationary solution.

Advantages of suggested modified schemes have been shown in the stationary and non stationary problems. In the schemes with the second order of approximation the special smoothing operators are introduced for oscillation recovery. Modified schemes have been generalized to the case of arbitrary two-dimensional curvilinear coordinates. Program systems have been created for solving of the internal aero dynamical problems in the approximation of Navier-Stokes equations. Two-dimensional numerical computations of viscous heat-conducted supersonic gas flows have been realized. Behaviors of flows for different flows parameters and channel forms have been achieved. Analysis of modified schemes and realized numerical computations of one-dimensional and two-dimensional flows allows to draw a conclusion about the efficiency of offered approach and adaptability of considered algorithms for computation of complex flows in many-dimension problems.

The work is realized using partial financial support of RFFI (project code 05-01-00146a) and Integration project SB RAS #116.

Note. Abstracts are published in author's edition

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