卷 11, 编号 5 (2019)

The paper proposes a difference scheme for the equations of an isentropic ideal gas on triangular meshes. The scheme satisfies the mass conservation law and guarantees the positiveness of the density function. The solution of the scheme satisfies the energy inequality. The solution of the scheme is proven to exist.

A numerical model describing the dynamics of the surface gravity waves and acoustic waves induced in the ocean by small dynamic deformations of the bottom is developed. The model is based on the linear potential theory. The model represents a combination of two dynamically coupled blocks: deep-water and shallow. The deep-water block solves a three-dimensional problem of potential wave theory in the sigma-spherical coordinates; the shallow block solves a two-dimensional problem of shallow water theory in the spherical coordinates. The results of testing the numerical model using the analytical solution of the problem for the flat horizontal bottom are presented. A comparative analysis of the simulation results of tsunamis on November 15, 2006 and January 13, 2007 on the Central Kuril Islands with the use of the newly developed and conventional long-wave models is performed.

A transient mathematical model for modeling the transport of cuttings in the drilling mudflow during drilling horizontal and directional wells is presented. The model is based on a two-layer model that takes into account the cuttings in the fluid flow and the motionless cutting substrate. The relationships for calculating the mass exchange between the substrate and the cuttings in the flow, the friction and heat transfer between the cuttings and the fluid flow, as well as the heat transfer between the fluid and the substrate with the annulus. Options for simulating Newtonian and non-Newtonian fluid motion are implemented. It is assumed that the fluid moves in the annular channel formed by the well wall and the drill string. The presence of eccentricity in the channel is taken into account. To simulate the motion and heat transfer, a system of mass, momentum, and energy equations is solved for each component separately. The numerical implementation is based on the finite volume method, the convective terms are written in the counterflow form. The results of the test calculations demonstrating the efficiency of the model proposed are presented. The problem on the displacement of cuttings from an arbitrarily oriented well is considered.

In this article, we describe a new mathematical model (bifurcational turbulence model) and justify its suitability for the prediction of laminar and turbulent boundary layer characteristics. The main specific feature of the model is the laminar-turbulent transition, arising as a new solution of the equation for Reynolds stresses, closing the system of Reynolds-averaged Navier-Stokes (RANS) equations. The article is divided into three main parts. The first part describes the RANS and second-order closure conditions together with the premises that we use to obtain the model equations in the closed form. In the second part, we derive the equations of the turbulent-flow model in the shear layer. In the third part, we consider the boundary-layer turbulence transition over a flat plate and present the results of numerical simulations compared with the experimental data.

A mathematical model of the flow of a polyatomic gas containing a combination of the Navier-Stokes-Fourier (NSF) model and the model kinetic equation of polyatomic gases is presented. At the heart of the composed components is a unified physical model, as a result of which the NSF model is a strict first approximation of the model kinetic equation. The model allows calculations of flow fields in a wide range of Knudsen numbers (Kn), as well as fields containing regions of a high degree of dynamic nonequilibrium. The boundary conditions on a solid surface are set at the kinetic level, which allows, in particular, to formulate the boundary conditions on the surfaces absorbing or emitting gas. The composed model was tested. The example of the problem of the shock wave profile shows that up to Mach numbers M ≈ 2 the combined model gives smooth solutions even in those cases where the sewing point is in a high gradient region. For the Couette flow, smooth solutions are obtained at M = 5 and Kn = 0.2.

The special features of the computer simulations of the radiation heat exchange calculations of spacecraft (SC) with a specular-diffuse approximation of the nature of the surface reflection according to the algorithms, which directly calculate the radiation exchange factors by the Monte Carlo (MC) method, and according to the author’s algorithm, which calculate them by determining the specular exchange factors of the absorbed radiation, are considered. The effects of approximating the model’s geometric surface approximation method and calculation algorithm on the results of calculating the fluxes and temperature are shown.

The paper is devoted to the mathematical modeling of flows within discrete fracture network systems, taking into account the fluid flow along vugs associated with fracture intersections. A mathematical model is described for a two-phase flow accounting for the flow exchange between fractures and vugs, as well as capillary and gravitational forces. Capillary forces are characterized by the Young–Laplace model which takes into account rock wettability, surface tension, fracture aperture, and vug cross-section diameters. The appropriate numerical simulation techniques are presented. Under various wettability conditions, the effect the flow within vugs has on the water–oil displacement process in a fractured vuggy reservoir is numerically investigated. It is shown that the presence of vugs at the intersections of fractures may significantly influence the flow characteristics under certain conditions.

Based on a modified two-equation model of turbulence, the numerical model of the dynamics of a cylindrical localized zone of turbulent mixing in a longitudinal uniform shear flow of homogeneous fluid is constructed. The results of the numerical experiments demonstrate significant turbulent energy generation caused by the effect of the shear flow. The question of the similarity of the flow with respect to the shear Froude number is considered. The results of the numerical experiments show the similarity of the flow for large values of this parameter, which correspond to small values of the velocity gradients of the shear flow.

A The paper presents theoretical analysis of a two-phase medium model for describing shock-wave processes in dense gas particle mixtures, taking into account the chaotic motion and collisions of particles. Hyperbolicity regions and composite-type domains are identified in the governing system of equations. It is shown that the hyperbolicity region expands beyond the collisionless model. An approximate hyperbolized model is presented. Numerical solutions of the problem on the development of various shock-wave structure types are compared. The convergence properties in numerical simulations of non-conservative composite-type equations were established using the Harten and Gentry–Martin–Daly schemes. The conditions of the hyperbolized model applicability to different types of flows are obtained. It is shown that, in the general case, shock-wave processes in gas suspensions should preferably be analyzed within a complete model.

The aim of this work is to study the uniformity of the treatment of coatings with an anti-icing liquid reagent using mathematical methods. The task of the modeling presented is to formulate the basic principles for the development of mathematical support and software for monitoring systems of road and airfield machines for the distribution of reagents. To do this, a mathematical model for the motion of droplets of a liquid anti-icing reagent in the air, taking into account the effect of the wind and the physical properties of the medium under consideration, is proposed. The original program code is developed based on it in the QtOctave environment. Using computer simulation, the influence of the height of the installed working element of the machine, i.e., the distributing disk, on the spraying density of the reagent is investigated. The QtOctave software product allows showing the plot of dependence of the uniform distribution of droplets over the length of the treated zone on the wind velocity. The character of the influence of the direction of the motion of air mass on the nonuniform settling of the reagent’s droplets on the coating is revealed. The calculation plot and results confirming the absence of relationships between the rotational speed of the drive shaft of the disk and deviation from the uniform distribution of droplets in the process of the anti-ice treatment of the airfield and road surfaces are presented. The numerical and analytical results should be used in the work of monitoring systems, the main purpose of which is to ensure the uniform dispersion of the reagent with an assigned range and flow rate.