Visualization of flows of a viscous conductive liquid with the presence of impurities in the flow field corresponding to exact solutions of the MHD equations

Abstract

A system of equations for the magnetic hydrodynamics (MHD), supplemented by the convection-diffusion equation describing the flow of a viscous conducting incompressible flu-id taking into account the presence of impurities in it is considered in this paper. Modern sci-entific visualization software, such as ParaView, provide a wide range of possibilities for visu-alization and, therefore, a clearer presentation of the structure of such flows, especially in three-dimensional case. This opportunity allows to analyze, draw conclusions, note the fea-tures of the investigated fluid flows, and was actively used in the preparation of this publica-tion. The MHD model is an active field of research for many scientists, however, most of the works are devoted exclusively to numerical modeling, and very little attention has been paid to exact solutions for these problems. The article discusses classes of exact solutions of the MHD equations and the associated convection-diffusion equation. The exact solutions found can be used for verification of developed numerical algorithms for solving the discussed prob-lems. Moreover, the exact solutions found describe fluid flows in a porous medium and are related to the development of a core simulator that will allow to simulate intraplast effects. It is associated with the creation of a domestic technology "digital field" and the tasks of con-trolling the parameters of incompressible liquids. For the oil and gas industry, a solution of this class of task will allow to perform optimization effects of various types (mechanical, elec-tromagnetic, thermal, etc.) in order to increase the oil recovery factor.