# numerical method

## 3D model and numerical algorithm for gas filtration in porous media

The article presents a three-dimensional mathematical model of the gas filtration process in porous media and a numerical algorithm for solving the initial-boundary value problem.  The developed model is described using the nonlinear differential equation in partial derivatives with the appropriate initial and boundary conditions.  The proposed mathematical apparatus makes it possible to carry out hydrodynamic calculations taking into account changes in the main factors affecting the process under consideration: permeability, porosity, and thickness of layers, gas recovery coefficient, visc

## Calculation model for the evaluation of tired defect development in the freight wagon side frame

The reliability and safe operation of mechanical elements of rail transport is an important and relevant scientific and technical issue since high-loaded units and elements of its chassis are exposed to prolonged operation and their failure can lead to damage with catastrophic consequences. To prevent the possible failure of such objects, there is a necessity for a reliable estimation of their residual life.

## Construction of skeletal curves elastic coupling with a near-zero or negativ inflexibility

The resilient muff of a near-zero inflexibility is considered. The dependence and method of mounting of muff’s resilient moment are given. The simple but effective numerical method for the construction of skeletal curves is suggested. It is shown that a skeletal curve for a muff with the area of negative inflexibility has two branches.

## Models of mass transfer in gas transmission systems

The models of gas movement in pipelines and gas filtration processes in complex porous media are considered in entire and fractional derivatives. The method for linearization of equations, which are included in the mathematical model of mass transfer, is suggested as well as an iterative scheme for solving initial systems of nonlinear differential equations is constructed. The finite-element model of the problem with the use of the Petrov-Galerkin method and Grunwald-Letnikov scheme concerning derivatives of the fractional order are implemented.