Modeling of compressible magnetohydrodynamic turbulence in electrically and heat conducting fluid using large eddy simulation

Many electrically and heat conducting fluid flows cannot be described within the framework of incompressible medium or by compressible magnetohydrodynamic equations on the assumption of polytropic (or adiabatic) process. Therefore, we consider a heat conducting compressible fluid with the use of an energy equation. Application of large eddy simulation approach to heat conducting compressible magnetohydrodynamics is considered. The system of the filtered magnetohydrodynamic equations with the total energy equation using the mass-weighted filtering procedure has been obtained. It is shown that novel subgrid-scale terms arise in the Favre-filtered equations due to the presence of a magnetic field in the total energy equation. Parametrizations of these extra terms are developed. In order to derive these subgrid-scale terms, we use an approach based on generalized central moments. Computations at various Mach numbers are made for decaying compressible magnetohydrodynamic turbulence. The obtained numerical large eddy simulation results are analyzed on the basis of comparison with results of numerical experiments performed by direct numerical simulation. Validity of large eddy simulation method is thus demonstrated. It is shown that consideration of the subgrid-scale terms in the total energy equation scarcely affects the kinetic and the magnetic energy for low and even high Mach number, while for the temperature the presence of subgrid-scale models in the energy equation is an important condition for improvement in calculation accuracy of thermodynamic quantities. The technique with the mass-weighted filtering and with the use of various types of subgrid-scale models provides good calculation accuracy for different problems for compressible fluid in the absence of discontinuities, associated with the appearance of shocks, in other words, when the value of the Mach number is low or moderate (that is, the flow is subsonic). For supersonic magnetohydrodynamic flows, it is necessary to use special numerical methods.