Numerical Study of a Flow of Viscoelastic Fluid of Kelvin - Voigt Having Zero Order in a Magnetic Field

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.