Vol 4, No 20 (2016)
- Year: 2016
- Published: 17.12.2016
- Articles: 10
- URL: https://ogarev-online.ru/2311-2468/issue/view/18877
Full Issue
Modeling of material point flight with variable coefficient of air resistance
Abstract
The paper deals with the movement of material point in the atmosphere of constant or variable density. The point is supposed to be under the action of gravity and air- resistance forces, and the resistance coefficient of the point depends on its velocity. The relation between the range, the launch angle and the initial velocity of the point is found.
Using Chombo library for solving problems of heat and mass transfer on locally-adaptive refined grids
Abstract
The paper deals with the methodology of solving equations of heat and mass transfer on orthogonal local-adaptive grids by the discontinuous Galerkin method and Chombo library. Numerical schemes for solving the equations of gas dynamics and the equation of heat conduction are considered. The schemes of transmitting the values of grid functions from one level of adaptation to another are described. The algorithm of constructing the grid around the body of given geometry for external aerodynamics problems is included.
Implicit scheme based on discontinuous Galerkin method for modeling temperature in oil reservoir
Abstract
The implicit scheme is developed to simulate the temperature in the "well- fracture-layer" system. The scheme is based on the discontinuous Galerkin method. The two- dimensional heat conduction equation with constant coefficients equal to unity is considered. The expressions to determine matrix elements of the system of linear equations are obtained.
Sequence density and its role in number theory
Abstract
In 1930 the Soviet scientist L. G. Shnirelman first began to consider the sequence density a measure of "density" of numerical sequences. Consequently, many of the classic problems of the number theory got more elegant formulations and proofs. This paper considers the concept of sequence density and proves its basic properties. The examples illustrating the sequence density calculation are included.
Dynamics of points in Reuleaux triangle
Abstract
The paper studies a one-parametric family of trajectories of points in the Reuleaux triangle formed by its rolling within a square. The bifurcation values that determine the qualitative behavior of the trajectory are found. The trajectory components, their number and equations are determined. For all values that are greater than the first bifurcation value a ratio of an area of a figure’s square bounded by the trajectory and its circumscribed square area is calculated. The best approximation to a square is found.
Simulation of non-viscous gas flow with pollutant transfer at wind grab
Abstract
The paper describes a model of non-viscous gas flow through the system of Navier-Stokes equations and the continuity equation for the concentration of the pollutant with the boundary condition of the wind grab from the ground. The study includes the calculation results of a numerical algorithm based on sampling of the obtained equations on structured grid by the finite volume method.
Formation of math model for assessment of enterprise financial condition
Abstract
The article deals with the formation of a mathematical model for assessment of the financial condition of an enterprise by the least square method. This mathematical model allows to calculate the elements of assets and liabilities of the balance sheet. The suggested approach allows to identify the factors contributing to the increase of efficiency of the enterprise activities.