Информационная система "Конференции"

Abstracts

Numerical solution of differential and integral equations

The initial boundary value problem for the two-dimensional Navier-Stokes equations written in terms of "eddy-current" variables is considered in the closed region, some boundaries of which are rigid walls. On the basis of the splitting method with respect to physical processes (convection and diffusion) an effective numerical method is proposed for solving the problem. Since the original problem formulation does not contain boundary conditions for vorticity on rigid walls in explicit form, the finite-difference boundary conditions (Woods formula) are used here to evaluate vorticity. It was shown in [1] that in the case of use of second-order schemes Woods conditions do not improve essentially the numerical-solution accuracy in comparison with Thom conditions. In the present paper the finite-difference problem is formulated on the basis of fourth-order schemes at the diffusion stage. The stability of the sweep method (Thomas algorithm) at the convection stage is analysed, the stability of the finite-difference initial boundary value problem at the diffusion stage is proved, the test problem is calculated. The results of test calculations demonstrate the convergence of numerical solution with the third order. [1] Voevodin A.F., Protopopova T.V. Numerical method for viscous flows in closed regions// Siber. J. Indust. Math., 2001, v. 4, N 1 (7), pp. 29-37.

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