Том 10, № 6 (2018)

The finite difference scheme for modeling seismo-acoustic field propagation in axisymmetric absorbing media excited by an emitter in the borehole fluid (a monopole, a dipole, or a quadrupole) during the acoustic logging, or by an emitter in an elastic medium (a concentrated force, a dipole, or a center of expansion) during the seismic prospecting is presented. The explicit finite difference scheme approximating the equations of the modified Biot’s model, which describes the acoustic wave propagation in an isotropic porous viscoelastic medium saturated with viscous fluid, is proposed.

In this paper, we present a turbulent combustion model for calculating self-oscillations in combustion chambers. The model is based on the large eddy simulation (LES) method in conjunction with the global methane combustion mechanism. We numerically simulated self-oscillations in a laboratory combustion chamber. The fist longitudinal mode of oscillations is shown to be correctly predicted by modeling.

The article presents part of an ongoing investigation into the development of the magnetorotational instability (MRI) on a laboratory setup using computational experiments. The instability of the rotational flow of liquid sodium in a ring channel is studied. This flow is simulated at more realistic values of the Reynolds number in order to determine the dependence of the MRI parameters on the viscosity coefficient of the flow.

A Monte Carlo model is developed for an experiment on measuring the neutron lifetime by the method of ultracold neutrons (UCNs) in a material storage trap. The trajectory of each neutron is calculated with allowance for gravity. The model fully reproduces all stages of the experiment. The necessary statistics are compiled by calculations on a computer cluster. The calculation results demonstrate the agreement between the calculated and experimental time dependences of the detector count and determine the systematic uncertainty associated with the method for calculating the effective collision frequency of ultracold neutrons in a trap. The simulation of all details of this experiment is extremely important for substantiating the attained accuracy and for proving the absence of systematic errors.

The generalized fractional Brownion motion (gfBm) is a new extension of both fractional and sub-fractional Brownian motions, introduced very recently. We show that this process could serve to obtain new models, better than those constructed from fractional and sub-fractional Brownian motions, permitting to take the level of correlation between the increments of the studied phenomenon into account. We also expand explicitly this process, we study the rate of convergence of the obtained expansion and, we apply our result to get a computer generation of some gfBm sample paths. In particular we present some sample paths of the even and odd parts of the fractional Brownian motion.

Side weirs are installed on the main channels wall in sewage disposal systems and irrigation networks to divert the flow. In this paper, the flow pattern in rectangular channels along a side weir is predicted using the Volume of Fluid (VOF) scheme and the standard k–ε and RNG k–ε turbulence models. A comparison between the numerical and experimental results shows the high accuracy of the numerical model. For example, the values of root mean square error (RMSE), mean absolute relative error (MARE) and correlation coefficient (R) for the lateral velocity on z = 0.183 m level are calculated 3.782, 0.399 and 0.993, respectively. According to the simulation results, as the flow approaches to the side weir plane the flow field pressure decreases suddenly and at the end of the side weir the pressure increases. Also, by advancing the flow towards the downstream of the side weir the turbulent kinetic energy of the flow within the rectangular channel decreases. For all levels, the turbulent length scale value suddenly increases by reaching the flow to the end of the side weir.