A. S. Petrosyan

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.

Large-Eddy Simulations of Magnetohydrodynamic Turbulence in Heliophysics and Astrophysics

We live in an age in which high-performance computing is transforming the way we do science. Previously intractable problems are now becoming accessible by means of increasingly realistic numerical simulations. One of the most enduring and most challenging of these problems is turbulence. Yet, despite these advances, the extreme parameter regimes encountered in space physics and astrophysics (as in atmospheric and oceanic physics) still preclude direct numerical simulation. Numerical models must take a Large Eddy Simulation (LES) approach, explicitly computing only a fraction of the active dynamical scales. The success of such an approach hinges on how well the model can represent the subgrid-scales (SGS) that are not explicitly resolved. In addition to the parameter regime, heliophysical and astrophysical applications must also face an equally daunting challenge: magnetism. The presence of magnetic fields in a turbulent, electrically conducting fluid flow can dramatically alter the coupling between large and small scales, with potentially profound implications for LES/SGS modeling. In this review article, we summarize the state of the art in LES modeling of turbulent magnetohydrodynamic (MHD) flows. After discussing the nature of MHD turbulence and the small-scale processes that give rise to energy dissipation, plasma heating, and magnetic reconnection, we consider how these processes may best be captured within an LES/SGS framework. We then consider several specific applications in heliophysics and astrophysics, assessing triumphs, challenges, and future directions.

Particular solutions of shallow-water equations over a non-flat surface

Abstract It is shown that the generalization of elementary solutions of the classical shallow water equations to the case of a non-flat surface is possible only for the class of underlying surfaces for which simple wave solutions exist, namely for slopes of constant inclination. The simple selfsimilar solutions for the shallow-water equations over slopes are obtained and the principal nonexistence of simple wave solutions was shown for other surfaces. It is shown that the characteristics of the equations over an oblique plane are branches of parabolas that have second-order contact with the characteristics of an appropriate system of shallow-water equations over the flat surface. As a consequence, shallow water physics on slopes is essentially different. The coordinate transformation that transforms the one-dimensional Saint–Venant system of equations to that for the classical shallow-water equations is found and sufficient conditions for the existence of this transformation are obtained.

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.

The initial discontinuity decay problem for shallow water equations on slopes

Abstract The initial discontinuity decay problem for shallow water equations on slopes is formulated and solved. The nondegenerate transformation of dependent and independent variables that reduces the Saint–Venant equations on slopes to the classical shallow water equations on flat plates is used. The solution of a basic initial discontinuity decay problem for the classical equations of shallow water above a homogeneous surface is provided. The independent derivation of this solution here is directed first of all on mathematicians and physicists because, for one reason, it enables generalisations to more complicated geometries.

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.