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The unique solvability of stationary and non-stationary incompressible melt models in the case of their linearization

Kazhikenova Saule Sh.

Archives of Control Sciences

2021

Vol. 31, No. 2

307--332

The article presents ε-approximation of hydrodynamics equations’ stationary model along with the proof of a theorem about existence of a hydrodynamics equations’ strongly generalized solution. It was proved by a theorem on the existence of uniqueness of the hydrodynamics equations’ temperature model’s solution, taking into account energy dissipation. There was implemented the Galerkin method to study the Navier-Stokes equations, which provides the study of the boundary value problems correctness for an incompressible viscous flow both numerically and analytically. Approximations of stationary and non-stationary models of the hydrodynamics equations were constructed by a system of Cauchy-Kovalevsky equations with a small parameter ε. There was developed an algorithm for numerical modelling of the Navier-Stokes equations by the finite difference method.

Modelling of fluid flow in the steel continuous casting process

Rywotycki M., Malinowski Z.

Metallurgy and Foundry Engineering

2004

Vol. 30, No 2

99-108

The paper presents the mathematical model describing the fluid flow. The motion of liquid metal in the steel continuous casting mould has been analysed. The solution for the velocity field has been obtained from the Navier-Stockes equation and the continuity condition. The problem has been solved with the use of the finite element method. In the course of numerical calculations, the velocity fields for various dimensions of the casted strip and various casting velocity were obtained. The liquid, mushy and solid zones were taken into consideration in the model.

W pracy przedstawiono model matematyczny opisujący ruch cieczy. Analizie został poddany ruch ciekłego metalu w krystalizatorze COS. Opis pola prędkości otrzymano z rozwiązania równania Naviera-Stokesa z równaniem ciągłości strugi. Przedstawiony problem został rozwiązany z zastosowaniem metody elementów skończonych. W trakcie obliczeń numerycznych otrzymano pola prędkości dla różnych wymiarów pasma COS i różnych prędkości odlewania. Obszar obliczeń podzielono na strefy: ciekłą, przejściową i zakrzepłą.