K. V. Karelsky

Development of large eddy simulation for modeling of decaying compressible magnetohydrodynamic turbulence

The large eddy simulation technique is developed for the study of decaying compressible magnetohydrodynamic turbulence. In the present paper the obtained results of numerical computations for large eddy simulation are compared with the results of direct numerical simulation of three-dimensional compressible magnetohydrodynamic turbulence under various similarity parameters, namely, magnetic Reynolds numbers, hydrodynamic Reynolds numbers, and Mach numbers. The comparison of five subgrid-scale closures of large eddy simulation for the magnetohydrodynamic case is made. The comparison between large eddy simulation and direct numerical simulation is carried out regarding the time evolution of kinetic and magnetic energy, cross helicity, subgrid-scale and molecular dissipations for kinetic and magnetic energy, turbulent intensities and quantities that describe anisotropy of flow, that is, skewness and kurtosis of velocity and magnetic field. It is shown that some subgrid-scale models proposed in the paper prov...

Large-eddy simulation of magnetohydrodynamic turbulence in compressible fluid

In the present article, the large eddy simulation (LES) technique for the study of compressible magnetohydrodynamic turbulence is developed. The filtered equations of magnetohydrodynamics of compressible fluid are obtained with the use of a mass-weighted filtering procedure (Favre filtering). Favre-filtered equations for large-scale components of turbulence include subgrid-scale terms describing subgrid phenomena. Different models for closure of subgrid terms are suggested. In this work numerical simulation of filtered magnetohydrodynamic equations and an analysis of the received characteristics of turbulent flow is carried out. The obtained results of numerical computations for different LES models are compared with the results of direct numerical simulation.

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 larg...

Subgrid-scale modeling of compressible magnetohydrodynamic turbulence in heat-conducting plasma

A large-eddy simulation (LES) approach for compressible magnetohydrodynamic (MHD) turbulence in heat-conducting plasma is developed for the first time. Subgrid-scale models for new terms appearing due to the presence of magnetic field are suggested. Results of modeling for decaying compressible MHD turbulence are presented. Comparison and testing with results obtained by direct numerical simulation are made. The efficiency of the developed LES technique for compressible MHD turbulence in heat-conducting plasma is shown.

Forced turbulence in large-eddy simulation of compressible magnetohydrodynamic turbulence

We present the large-eddy simulation method for studying forced compressible magnetohydrodynamic turbulence. The proposed method is based on a solution of the filtered basic equations of magnetohydrodynamics by finite-difference methods and on a linear representation of the driving forces in the momentum conservation equation and the magnetic induction equation. These forces supply the production of kinetic and magnetic energies. The emphasis is placed upon the important, and not investigated, question about the ability of the large-eddy simulation approach to reproduce Kolmogorov and Iroshnikov–Kraichnan scale-invariant spectra in compressible magnetohydrodynamic flows.

Nonlinear dynamics of magnetohydrodynamic flows of a heavy fluid in the shallow water approximation

The system of the magnetohydrodynamic equations for a heavy fluid has been analyzed in the shallow water approximation. All discontinuous self-similar solutions and all continuous centered self-similar solutions have been found. It has been shown that magnetogravity compression waves are broken with the formation of a magnetogravity shock wave. The initial decay discontinuity problem for the magnetohydrodynamic equations has been solved in the explicit form in the shallow water approximation. The existence of five different configurations implementing the solution of the decay of an arbitrary discontinuity has been demonstrated. The conditions necessary and sufficient for the implementation of each configuration have been found.

Subgrid-scale modelling in large-eddy simulations of compressible magnetohydrodynamic turbulence

In this paper we develop the method of large-eddy simulation (LES) for the full system of magnetohydrodynamics equations for a compressible fluid. We obtain filtered magnetohydrodynamics equations for a compressible fluid using the mass-weighted filtration procedure (Favre filtration). Favre-filtered equations for a large-scale turbulent component comprise terms describing subgrid-scale phenomena. These may be either entirely new terms for the energy equation or combinations of already known terms from models for a neutral compressible gas and models for an incompressible magnetic fluid. In the given paper we propose parametrizations of subgrid-scale terms.

THREE-DIMENSIONAL MODELING OF COMPRESSIBLE MAGNETOHYDRODYNAMIC TURBULENCE IN THE LOCAL INTERSTELLAR MEDIUM

We apply the large eddy simulation technique to carry out a three-dimensional numerical simulation of compressible magnetohydrodynamic turbulence in conditions relevant to the local interstellar medium. In accord with the large eddy simulation method, the large-scale part of the flow is computed directly and only small-scale structures of turbulence are modeled. The small-scale motion is eliminated from the initial system of equations of motion by filtering procedures, and its effect is taken into account by special closures referred to as the subgrid-scale models. Establishment of the weakly compressible limit with a Kolmogorov-like density fluctuation spectrum is shown in the present work. We use our computation results to study the dynamics of the turbulent plasma beta and anisotropic properties of the magnetoplasma fluctuations in the local interstellar medium.

Nonlinear dynamics of magnetohydrodynamic shallow water flows over an arbitrary surface

The magnetohydrodynamic equations system for a heavy fluid over an arbitrary surface in shallow water approximation is studied. All self-similar discontinuous and continuous solutions are found. The exact explicit solutions of the initial discontinuity decay problem over a flat plane and a slope are found. It is shown that the initial discontinuity decay solution is represented by one of five possible wave configurations. For each configuration the necessary and sufficient conditions for its realization are found. The changes in dependent and independent variables transforming the initial equations over a slope into those over a flat plane are found.

A finite-difference representation of the Coriolis force in numerical models of Godunov type for rotating shallow water flows

Abstract A finite-difference representation describing the Coriolis force in numerical methods of the Godunov type for flows of rotating shallow water is proposed in the paper. Finite-difference schemes are proposed for modelling flows both on a flat bed and on a bed of an arbitrary profile. The influence of the Coriolis force is simulated by introducing a fictitious unsteady boundary. The numerical algorithms developed here are based on representing an arbitrary bed surface and the Coriolis force by a complex unsteady step boundary. Due to inhomogeneity of the bed surface and the influence of the Coriolis force, a quasi-two-layer model of a liquid flow over a step boundary is used for numerical approximation of the source terms. The model takes into account the hydrodynamic peculiarities. This allows us to give a visual interpretation of nonlinear processes caused by inhomogeneity of the bottom and by the fictitious unsteady boundary describing the Coriolis force. The use of the quasi-two-layer model provides a better approximation to the original Euler equations in the presence of source terms. Comparative analysis of the well-known finite-difference schemes describing the rotation and inhomogeneity of the bottom surface profile is performed. Numerical calculations confirming the efficiency of the proposed method are also performed.