Browsing by Author "Kuttykozhaeva Sh. N."

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    Mathematical Modelling of Hydrodynamics Problems by the Method of Fictitious Domains
    (Suleyman Demirel University, 2012) Kuttykozhaeva Sh. N.
    This paper investigates the method of fictitious domains for solving boundary value problems in hydrodynamics, extending its application to nonlinear elliptic equations. A rigorous justification of the method is presented, and a new approach to achieve the best possible convergence rate from the auxiliary problem to the original problem is proposed. The study demonstrates that as the small parameter tends to zero, the solution of the fictitious domain problem converges to the generalized solution of the original boundary value problem. The theoretical results include existence, uniqueness, and stability estimates, providing a solid mathematical foundation for applying the fictitious domain method in hydrodynamic modeling.
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    Numerical method for solving the equation of navier-stokes
    (Suleyman Demirel University, 2011) Kuttykozhaeva Sh. N.
    This article presents a numerical method for solving the Navier-Stokes equations based on a variant of the fictitious domain method with continuation of the leading coefficient. A key feature of the method is that the boundary of the auxiliary domain is defined using the tangential components of velocity and pressure. This allows the construction of an efficient iterative method for numerical calculations. It is shown that the rate of convergence of the iterative method is independent of variations in a small parameter. The proposed approach provides a reliable and effective tool for the numerical solution of linear stationary Navier-Stokes equations.