Computational Experiment for a Class of Mathematical Models of Magnetohydrodynamics

The first initial-boundary value problem for the system modelling the motion of the incompressible viscoelastic Kelvin - Voigt fluid in the magnetic field of the Earth is investigated considering that the fluid is under external influence. The problem is studied under the assumption that the fluid is under different external influences depending not only on the coordinates of the point in space but on time too. In the framework of the theory of semi-linear Sobolev type equations the theorem of existence and uniqueness of the solution of the stated problem is proved.The solution itself is a quasi-stationary semi-trajectory. The description of the problem's extended phase space is obtained.The results of the computainal experiment are presented.

Keywords

magnetohydrodynamics; Sobolev type equations; extended phase space; incompressible viscoelastic fluid; explicit one-step formulas of Runge - Kutta.

References

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5. Kondyukov A.O., Kadchenko S.I., Kakushkin S.N. Numerical Modelling of the Motion of the Viscoelastic Conductive Fluid in the Magnetic Field. The copyright holder: Federal state budgatary educational institution of higher education 'Yaroslav-the-Wise Novgorod State University' (RU), № 2016619268, registered 17.08.2016, the registry of computer programs.