Large Eddy Simulations of Compressible MHD Turbulence in Heat-Conducting Fluid

摘要

We develop the large eddy simulation (LES) method for study of compressible magnetohydrodynamic (MHD) turbulence in heat-conducting fluid. Turbulent flows in a magnetic field are common both in applied areas and in physics of astrophysical and space plasma. Among the engineering applications, possibility of boundary layer control and drag reduction, MHD flow in a channel (for steel-casting processes) and in a pipe (for cooling of nuclear fusion reactors) can be mentioned. In the previous works authors used LES approach for study of incompressible MHD turbulent flow [1] and already applied LES technique for compressible MHD flow of polytropic gas [2-5]. However, in all mentioned papers MHD equations without the equation of energy balance are considered. Applications of LES technique to heat-conducting compressible MHD flows are significantly more difficult due to the increased complexity introduced by the need to solve the energy equation. This introduces novel subgrid-scale (SGS) terms due to the presence of magnetic field in total energy equations. We develop parameterizations for these SGS stresses in present work. Computations at various Mach numbers are performed for three-dimensional decaying compressible MHD turbulence. Validity of developed LES method is demonstrated by comparison with the direct numerical simulation (DNS) results.