Volume 9, Nº 4 (2017)

Numerical methods for solving equations of two-phase hydrodynamics, which describe the flow of a dispersed solid and gas mixture are considered. The Godunov method is applied as the main approach to approximate numerical fluxes in solutions of the relevant Riemann problems. The formulations of these problems for the solid and gas phases are given, their exact analytical solution is described, and possible simplified approximate solutions are discussed. The obtained theoretical results are applied to the construction of a discrete model, which results in the generalization of the well-known Godunov-type and Rusanov-type methods to the case of nonequilibrium two-phase media. The numerical results involve the verification of the constructed methods on the analytical solutions of two-phase equations.

A modified two-dimensional two-phase mathematical model of forest wildfires propagation is considered. The model is based on the averaging of three-dimensional equations of two-phase medium over the height of the forest fuel (FF) layer and it includes the (k‒ε)-turbulence model with additional turbulence production and dissipation terms in the forest layer and the Eddy Break-up Model for the combustion rate in the gas phase. The developed model can be used to carry out numerical simulation of the forest fire-front propagation under the conditions of a heterogeneous FF distribution, the presence of obstacles to the fire propagation, and the wind effects. This model can be used for real-time computation of the fire propagation, for expert assessments of emergency situations, and for assessments of the damage caused by forest fires.

Highly accurate finite-difference schemes that are widely used in computational aeroacoustics and referred to as dispersion-relation-preserving (DRP) schemes are adapted for the simulation of viscous flows. The main result consists in the construction and verification of numerical boundary conditions on a solid body, artificial boundaries, and on their interface. Calculations are performed for several test problems, including dissipation of the Lamb–Oseen vortex and decay of the Taylor–Green vortex in two-and three-dimensional cases and in infinite and semi-infinite (open-outlet) plane channels.

A problem of identifying one particular or a few possible pollution sources that are responsible for the deterioration of the air quality as a result of exceeding the standards of the maximum permissible emissions is considered. A model problem for a group of spatially divided stationary permanent industrial sources is solved. A statement identifying the problem and a method to solve it using two architectures of artificial neural networks, Kohonen’s networks for learning vector quantization with fixed and adaptive structures, as well as adaptive resonance theory network for analog inputs (ART-2), are presented. The method consists of clustering the data provided by self-learning algorithms (unsupervised learning). Estimation equations are given and operation algorithms of Kohonen’s and adaptive resonance theory networks at different life cycle stages are described. The results of the solution of the model problem that are obtained using each network is performed are comparatively analyzed.

We consider methods that are the inverse of the explicit Runge–Kutta methods. Such methods have some advantages, while their disadvantage is the low (first) stage order. This reduces the accuracy and the real order in solving stiff and differential-algebraic equations. New methods possessing properties of methods of a higher stage order are proposed. The results of the numerical experiments show that the proposed methods allow us to avoid reducing the order.

This paper addresses the problem of heat transport in an elliptical channel in the presence of a temperature gradient parallel to its axis. The Williams equation is used as the basic equation describing the kinetics of the process and a model of diffusive reflection is used as the boundary conditions on the channel wall. The deviation of the gas condition from the equilibrium is assumed to be small. In order to find a linear correction to the local equilibrium function of distribution, a boundary problem consisting of a linear homogeneous partial differential equation of the first order with a homogeneous boundary condition has been built. The solution of the built boundary value problem has been found by the method of characteristics. The value of the heat flow through the cross section of the channel is found by using numerical procedures implemented by the computer algebra Maple 17 system. The results were compared with the analogous results found in the open press.