Kinetic consistent MHD algorithm for incompressible conductive fluids

Abstract

The first ideas concerning the principle of operation of non-mechanical magneto-hydrodynamic pumping systems were originally created at the end of the 1960s during studies of efficient heat exchange systems in nuclear energy sources using liquid metals as coolant. Currently, these ideas are of increasing interest in the creation of many critical technologies that require precise flow control in distributed energy transfer systems, in particular for a new generation of environmentally friendly efficient nuclear power sources.In this regard, computational fluid dynamic methods are an effective instrument for studying complex energy transfer processes, the possibilities of which have been significantly expanded with the creation of modern high-performance computing systems and modern computing technologies.The purpose of this article is to describe an advanced method of the mathematical modeling of magneto-hydrodynamic processes based on kinetic and kinetically consistent models. The novelty of this approach lies in more advanced physical models derived from the Boltzmann kinetic equation with a complex-valued statistical distribution function that includes electromagnetic interactions. The possibility of applying this description to incompressible viscous media (liquid metals) in complex magneto-hydrodynamic systems is shown.The system of equations of the proposed method, a numerical algorithm and the results of the mathematical modeling of a test system for energy transfer using a magneto-hydrodynamic pump and an exchange cavity are presented.