Details

Title

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

Journal title

Archives of Control Sciences

Yearbook

2021

Volume

vol. 31

Issue

No 2

Affiliation

Kazhikenova, Saule Sh. : Head of the Department of Higher Mathematics, Karaganda Technical University, Kazakhstan

Authors

Keywords

Navier–Stokes equations ; hydrodynamic ; approximations ; mathematical models ; incompressible melt

Divisions of PAS

Nauki Techniczne

Coverage

307-332

Publisher

Committee of Automatic Control and Robotics PAS

Bibliography

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[3] P.M. Gresho: Incompressible fluid dynamics: some fundamental formulation issues. Annu. Rev. Fluid Mech., 23, Palo Alto, Calif., (1991), 413-453.
[4] R. Lakshminarayana, K. Dadzie, R. Ocone, M. Borg, and J. Reese: Recasting Navier–Stokes equations. J. Phys. Commun., 3(10), (2019), 13– 18, DOI: 10.1088/2399-6528/ab4b86.
[5] S.Sh. Kazhikenova, S.N. Shaltakov, D. Belomestny, and G.S. Shai- hova: Finite difference method implementation for numerical integration hydrodynamic equations melts. Eurasian Physical Technical Journal, 17(1), (2020), 50–56.
[6] O.A. Ladijenskaya: Boundary Value Problems of Mathematical Physics. Nauka, Moscow, 1973.
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[9] K. Yasumasa and T. Takahico: Finite-element method for three-dimensional incompressible viscous flow using simultaneous relaxation of velocity and Bernoulli function. 1st report flow in a lid-driven cubic cavity at Re = 5000. Trans. Jap. Soc. Mech. Eng., 57(540), (1991), 2640–2647.
[10] H. Itsuro, Î. Hideki, T. Yuji, and N. Tetsuji: Numerical analysis of a flow in a three-dimensional cubic cavity. Trans. Jap. Soc. Mech. Eng., 57(540), (1991), 2627–2631.
[11] X. Yan, L. Wei, Y. Lei, X. Xue, Y.Wang, G. Zhao, J. Li, and X. Qingyan: Numerical simulation of Meso-Micro structure in Ni-based superalloy during liquid metal cooling. Proceedings of the 4th World Congress on Integrated Computational Materials Engineering. The Minerals, Metals & Materials Series. Ð. 249–259, DOI: 10.1007/978-3-319-57864-4_23.
[12] T.A. Barannyk, A.F. Barannyk, and I.I. Yuryk: Exact Solutions of the nonliear equation. Ukrains’kyi Matematychnyi Zhurnal, 69(9), (2017), 1180–1186, http://umj.imath.kiev.ua/index.php/umj/article/view/1768.
[13] S. Tleugabulov, D. Ryzhonkov, N. Aytbayev, G. Koishina, and G. Sul- tamurat: The reduction smelting of metal-containing industrial wastes. News of the Academy of Sciences of the Republic of Kazakhstan, 1(433), (2019), 32–37, DOI: 10.32014/2019.2518-170X.3.
[14] S.L. Skorokhodov and N.P. Kuzmina: Analytical-numerical method for solving an Orr–Sommerfeld-type problem for analysis of instability of ocean currents. Zh. Vychisl. Mat. Mat. Fiz., 58(6), (2018), 1022–1039, DOI: 10.7868/S0044466918060133.
[15] N.B. Iskakova, A.T. Assanova, and E.A. Bakirova: Numerical method for the solution of linear boundary-value problem for integrodifferential equations based on spline approximations. Ukrains’kyi Matematychnyi Zhurnal, 71(9), (2019), 1176–1191, http://umj.imath.kiev.ua/index.php/ umj/article/view/1508.
[16] S.Sh. Kazhikenova, M.I. Ramazanov, and A.A. Khairkulova: epsilon- Approximation of the temperatures model of inhomogeneous melts with allowance for energy dissipation. Bulletin of the Karaganda University- Mathematics, 90(2), (2018), 93–100, DOI: 10.31489/2018M2/93-100.
[17] J.A. Iskenderova and Sh. Smagulov: The Cauchy problem for the equations of a viscous heat-conducting gas with degenerate density. Comput. Maths Math. Phys. Great Britain, 33(8), (1993), 1109–1117.
[18] A.M. Molchanov: Numerical Methods for Solving the Navier–Stokes Equations. Moscow, 2018.
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Date

2021.07.01

Type

Article

Identifier

DOI: 10.24425/acs.2021.137420
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