โ Scribed by V.I. Pinchukov
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A build-up scheme of the second order of approximation for calculating the stationary flows of a viscous gas is proposed. The stability of the scheme is proved, and the results of ~est calculations are given.
Implicit schemes of variable-direction type where the inverse operators are represented by three-diagonal matrices are widely used /1-5/.
The scheme proposed below is close to another type of iterative methods, such as the alternately-triangular method /6/, the Seidel method and the relaxation method based upon it, the Saul'ev method /8/, and the implicit twodiagonal method /9/.
Examples of the use of these methods to calculate the flow of a viscous heat-conducting gas are not very numerous. The Navier-Stokes equations are solved in /10/ and /11/ by the Seidel method, the scheme being conditionally stable for the model used. The build-up scheme in /12/ is designed to solve the one-dimensional Navier-Stokes equations. In /13/ and /14/ the flow of a viscous gas is studied by using an i~plicit two-stage scheme where the inverse operators are represented by block triangular matrices.
In the present paper it is proposed to solve the Navier-Stokes equations by an iterative scheme which, unlike that given in /13/ and /14/, has the property of complete approximation and has second-order accuracy.
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