The paper describes an explicit multi-dimensional numerical scheme for Special Relativistic Two-Fluid Magnetohydrodynamics of electron-positron plasma and a suit of test problems. The scheme utilizes Cartesian grid and the third order WENO interpolation. The time integration is carried out using the third order TVD method of Runge-Kutta type, thus ensuring overall third order accuracy on smooth solutions. The magnetic field is kept near divergence-free by means of the method of generalized Lagrange multiplier. The test simulations, which include linear and non-linear continuous plasma waves, shock waves, strong explosions and the tearing instability, show that the scheme is sufficiently robust and confirm its accuracy.

The evolution of a supernova remnant in a cloudy medium as a function of the volume filling factor of the clouds is studied in a three-dimensional axially symmetrical model. The model includes the mixing of heavy elements (metals) ejected by the supernova and their contribution to radiative losses. The interaction of the supernova envelope with the cloudy phase of the interstellar medium leads to nonsimultaneous, and on average earlier, onsets of the radiative phase in different parts of the supernova envelope. Growth in the volume filling factor f leads to a decrease in the time for the transition of the envelope to the radiative phase and a decrease in the envelopes mean radius, due to the increased energy losses by the envelope in the cloudy medium. When the development of hydrodynamical instabilities in the supernova envelope is efficient, the thermal energy falls as E t ∼ t −2.3 , for the propagation of the supernova remnant through either a homogeneous or a cloudy medium. When the volume filling factor is f > ∼ 0.1, a layer with excess kinetic energy andmomentumforms far behind the global shock front from the supernova, which traps the hot gas of the cavity in the central part of the supernova remnant. Metals ejected by the supernova are also enclosed in the central region of the remnant, where the initial (high) metallicity is essentially preserved. Thus, the interaction of the supernova envelope with the cloudy interstellar medium appreciably changes the dynamics and structure of the distribution of the gas in the remnant. This affects the observational characteristics of the remnant, in particularly, leading to substantial fluctuations of the emission measure of the gas with T > 10 5 K and the velocity dispersion of the ionized gas.

The aim of this work is to construct an algorithm for visualizing a polydisperse phase of solid particles (dust) in an inhomogeneous flow of a two-phase gas-dust mixture that would allow us to see, within one plot, the degree of polydispersity of the dust phase and the difference in the spatial distributions of individual fractions of dust particles in the computational domain. The developed technique allows us to reproduce concentrations from one to three fractions of dust particles in each cell in the computational domain. Each of the three fractions of dust particles is mapped to one of the main channels of the RGB palette.The intensity of the color shade is set to be proportional to the relative concentration of dust particles in this fraction. The final image for a polydisperse mixture is obtained by adding images in each of the three color channels. To visualize the degree of polydispersity, I propose depicting the spatial distribution of the entropy of the dust mixture. The definition of the entropy of a mixture is generalized to take into account the states of a mixture with zero number of particles in the mixture. They correspond to dust-free sections of the computational domain (voids). The proposed method for visualizing the polydispersity of a mixture of particles is demonstrated using the example of dynamic numerical modeling of the spatial features of dust structures formed in turbulent gas-dust flows and in flows with shock waves.Real liquid, gas or plasma media have an inhomogeneous structure and are complex, composite systems that include microobjects of different types and different nature, such as small solid suspended particles, droplets or bubbles. There are a huge number of areas in the field of technology in which a person deals with multiphase environments, from chemical reactors to engine building and aeronautics. There are no manifestations of polyphase in nature that are less significant. Despite the small relative mass content, impurity aerosol or dust particles can play an important role in the life of planetary atmospheres, interstellar or intergalactic gas. The dust component determines the optical properties of the medium, its opacity in one interval or another of the electromagnetic spectrum. As a consequence, dust in the atmosphere or in the interstellar gas can act as a coolant, realizing the anti-greenhouse effect [1,2]. Due to their windage, dust grains can cause an effective mechanical effect of star radiation on a transparent neutral gas, accelerating under the influence of radiation pressure and accelerating the surrounding matter [3,4]. Particles of dust in the interstellar gas act as a catalyst for the process of gas molecularization [1]. Dust also serves as a building material for the formation of solid celestial bodies, such as asteroids or planets [1].Examples of space objects enriched with impure dust particles are gas-dust interstellar clouds and nebulae, protoplanetary disks, spiral arms of galaxies and gas-dust halos of galaxies. Usually, cosmic dust grains are par...

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A large number of publications have been devoted to studying the features of the flow in two-phase flows in a gas-dispersed flow with inertial dust particles (shock waves, jets, turbulence, regular structures such as plasma crystals). In recent years, the study of the behavior of various fractions of impurity particles in polydisperse dust mixtures, expressed in the spatial separation of their distributions, has been of increasing interest. Spatial variations of individual components of the dust mixture make it possible to diagnose the state of the carrier gas phase in those cases when the carrier phase is very rarefied and cannot be observed directly (interstellar gas). This work is a continuation of the authors’ work [14], in which an original algorithm was proposed based on the use of three-dimensional color space resources, which allows visualizing spatial distributions of concentrations of up to three fractions of a polydisperse mixture of dust particles simultaneously, as well as an entropy measure that allows visualizing the degree of polydispersity in a heterogeneous gas-and-dust environment. However, the structural features of the impurity phase (caustics, areas of segregation of dust particles by their size, mass, etc.) are not necessarily spatially combined with its dynamic features (collisionless shock waves, flow turning points, stagnation points, accumulation points). In this paper, we propose a method for visualizing the dynamic features of a polydisperse collisionless mixture of particles in a two-phase gas-dust medium by constructing spatial distribution maps of the particle velocity dispersion anisotropy regions. Strong anisotropy of the velocity dispersion corresponds to the region in which an intense multi-stream flow occurs. Dust is considered as a mixture of several fractions, each of which contains particles of the same type, while the particle sizes in different fractions are different. For each dust fraction, a field is constructed of the spatial distributions of the eccentricities of the velocity dispersion ellipses. To visualize the degrees of anisotropy of the velocity dispersion of two fractions of a polydisperse dust mixture at once, a specially selected entropy measure is proposed. The results of two-dimensional demonstration calculations of a turbulent gas-dust medium and the anisotropy map in the distribution of the velocity dispersion of an impurity dust component are presented.