Abstract:
The article developed algorithms for the numerical solution of the initial-boundary problem of the flow of an incompressible viscoelastic Kelvin–Voigt fluid in the Earth's magnetic field. The theorem on an existence and uniqueness of this problem solution is proved using the theory of semilinear Sobolev type equations in the works written by T.G. Sukachev, S.A. Kondyukova. The original initial-boundary problem is transformed to the Cauchy problem for ordinary systems of nonlinear equations by sampling. Algorithms based on the explicit one-step schemes having Runge–Kutta type of seventh-order accuracy with a choice of integration step are used to find a numerical solution of the Cauchy problem. Evaluation of control of calculation accuracy at each time step is carried out by a scheme of the eighth order of accuracy. A time step is chosen according to the results of monitoring. Computational experiments show high computational efficiency of the developed algorithms for solving of the problem considered.
Keywords:
magnetohydrodynamics, incompressible viscoelastic fluid, explicit one-step formulas of Runge–Kutta, Sobolev type equations.
Citation:
S. I. Kadchenko, A. О. Kondyukov, “Numerical study of a flow of viscoelastic fluid of Kelvin–Voigt having zero order in a magnetic field”, J. Comp. Eng. Math., 3:2 (2016), 40–47
\Bibitem{KadKon16}
\by S.~I.~Kadchenko, A.~О.~Kondyukov
\paper Numerical study of a flow of viscoelastic fluid of Kelvin--Voigt having zero order in a magnetic field
\jour J. Comp. Eng. Math.
\yr 2016
\vol 3
\issue 2
\pages 40--47
\mathnet{http://mi.mathnet.ru/jcem62}
\crossref{https://doi.org/10.14529/jcem1602005}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3527955}
\zmath{https://zbmath.org/?q=an:06690885}
\elib{https://elibrary.ru/item.asp?id=26399836}
Linking options:
https://www.mathnet.ru/eng/jcem62
https://www.mathnet.ru/eng/jcem/v3/i2/p40
This publication is cited in the following 9 articles:
Zhiyong Si, Qing Wang, Yunxia Wang, “A rotational velocity‐correction projection method for the Kelvin–Voigt viscoelastic fluid equations”, Math Methods in App Sciences, 47:5 (2024), 3469
Y. Vinod, Suma Nagendrappa Nagappanavar, Sangamesh, K. R. Raghunatha, D. L. Kiran Kumar, “Unsteady triple diffusive oscillatory flow in a Voigt fluid”, J Math Chem, 2024
Y. Vinod, K. R. Raghunatha, Bassem F. Felemban, Ayman A. Aly, Mustafa Inc, Shahram Rezapour, Suma Nagendrappa Nagappanavar, Sangamesh, “Exploring double diffusive oscillatory flow in a Voigt fluid”, Mod. Phys. Lett. B, 2024
Mengmeng Duan, Yan Yang, Minfu Feng, “A weak Galerkin finite element method for the Kelvin-Voigt viscoelastic fluid flow model”, Applied Numerical Mathematics, 184 (2023), 406
T. G. Sukacheva, “Oskolkov models and Sobolev-type equations”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 15:1 (2022), 5–22
Zhiyong Si, Qing Wang, Yunxia Wang, “A modified characteristic projection finite element method for the Kelvin-Voigt viscoelastic fluid equations”, Computers & Mathematics with Applications, 109 (2022), 44
A O Kondyukov, T G Sukacheva, “Non-stationary model of incompressible viscoelastic Kelvin-Voigt fluid of higher order in the Earth's magnetic field”, J. Phys.: Conf. Ser., 1658:1 (2020), 012028
A. O. Kondyukov, T. G. Sukacheva, “A non-stationary model of the incompressible viscoelastic Kelvin–Voigt fluid of non-zero order in the magnetic field of the Earth”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 12:3 (2019), 42–51
A. O. Kondyukov, T. G. Sukacheva, S. I. Kadchenko, L. S. Ryazanova, “Computational experiment for a class of mathematical models of magnetohydrodynamics”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 10:1 (2017), 149–155
Citation in format AMSBIB
Contact us: