Abstract

The paper is devoted to the study and mathematical justification of the fictitious domain method for the Navier-Stokes equations. The method of fictitious domain with continuation by the lowest coefficients for the Navier-Stokes equations is substantiated in the work. The theorem of unambiguous solvability of the initial boundary value problem and the existence and uniqueness of the generalized solution of the auxiliary problem for the Navier-Stokes equations in the case of two spatial variables is proved. A numerical implementation of the proposed method of fictitious domain with continuation by the lowest coefficients for the Navier-Stokes equations is carried out. Various graphical illustrations of the results of numerical simulation using the fictitious domain method for the Navier-Stokes equations are presented.

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