| Реферат: | eng: Physical and mathematical models described by the Euler and Navier-Stokes equations for a compressible heat-conducting gas are widely used in numerical simulation in aerodynamics, power, environment protection, design of technical devices, and modelling of technological processes. Methods of finite difference and finite volumes became widespread in numerical solution of such models being most universal and suitable for solution of various classes of equations (see [1-11, 13-18]). The increase of dimensionality of problems and complexity of calculation domains imposed additional requirements on applied numerical algorithms. Those algorithms must provide necessary accuracy, be sufficiently stable, possess conservative properties, be economical with an ability to obtain a solution to the problem in reasonable time on available computers [7]. Application of explicit difference schemes for solution of Navier-Stokes equations may be inefficient because of strict restrictions on their stability especially in calculation of a stationary solution by the stabilization methods. Therefore, the solution of such problems is most often carried out by implicit difference schemes that are free from stability restrictions or have essentially weaker ones. Implicit difference schemes are constructed by factorization and splitting methods allowing one to reduce the solution of original many-dimensional problems to successive (or parallel) solution of their one-dimensional analogues, or problems of simpler structure (see [5, 6, 14, 18]). However, the introduction of splitting or factorization leads to appearance of additional terms of the second of higher orders in difference schemes, which can worsen the properties of numerical algorithms. Therefore, the problem of construction of economical algorithms remains to be one of the most important problems of numerical modelling.
In this paper we construct economical (in the number of operations per a grid node) numerical solution algorithms for the Euler and Navier-Stokes equations on the base of the splitting method, the ideology of its construction was described in [5, 6, 11]. The splitting technique was chosen for original equations so that the algorithms constructed on its basis were more economical than those proposed previously, possess a greater stability margin, and the influence of splitting was minimal.
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