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2 Archives of Control Sciences

2 2021

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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.

Difference melt model

Kazhikenova Saule Sh., Shaltakov Sagyndyk N., Nussupbekov Bekbolat R.

Archives of Control Sciences

2021

Vol. 31, No. 3

607--627

The basic objective of the research is to construct a difference model of the melt motion. The existence of a solution to the problem is proven in the paper. It is also proven the convergence of the difference problem solution to the original problem solution of the melt motion. The Rothe method is implemented to study the Navier-Stokes equations, which provides the study of the boundary value problems correctness for a viscous incompressible flow both numerically and analytically.