Vol 11, No 3 (2019)

This paper is devoted to the numerical simulation of isothermal moderately rarefied gas flows in three-dimensional spaces with a complex voxel geometry corresponding to the pore space of core (rock) samples. Classical Maxwell slip boundary conditions are used to take into account the slippage effect on the solid boundaries. The simulation results for several core samples under different averaged pressures are presented. The qualitatively correct dependence of the Klinkenberg slippage coefficient on the absolute intrinsic permeability is obtained.

An interpolative-characteristic method is constructed with the approximation not lower than the second order for solving the transport equation on an unstructured grid composed of tetrahedra. The problem of finding a numerical solution by this method, further referred to as the method of short characteristics, is subdivided into two subproblems. The first concerns the resolution of a single simplicial cell. A set of grid values must be specified, which when set on the illuminated faces is mathematically sufficient for obtaining all the remaining grid values in the cell. Depending on the location of the cell and the propagation direction of the radiation there are three different types of illumination. It is proposed to use interpolation of a cell in barycentric coordinates with 14 free coefficients, which enables taking into account the values of the radiation intensity at the nodes and the average integral values of the intensity over the edges and faces without adding new stencil points. This interpolation ensures at least the second order of approximation with additional allowance for the terms with the third-order approximation. Moreover, the method takes into account a conservative redistribution of the outbound flow over the edges of the cell. The second subproblem is associated with choosing the order of tracing the cell and can be solved using methods of graph theory. The numerical calculations confirmed approximately the second order of convergence.

A physicomathematical model of a two-phase liquid flow in a discrete fracture network—taking into account a nonuniform fracture aperture, flow exchange between fractures, capillary and gravitational forces—is presented. Capillary forces are described by the Young-Laplace model that takes into account the rock wetting angle and surface tension. The influence of the structure of the conducting channels in a fracture, capillary and gravitational forces, and the pressure gradient, as well as the water-and-oil viscosity ratio on the flow dynamics and the oil recovery factor, is explored. It is shown that capillary forces and the structure of channels in a fracture can play a decisive role in the process of oil displacement by water.

In this paper, we develop a coarse grained numerical model for the simulation of a self-organization process for a system of carbon nanotubes under the applied electric field. The model describes the polarization of nanotubes in the system with an electric field and also includes the Van der Waals interaction between nanotubes. We develop an iterative computation algorithm for particle charges in the nanotube, providing a significant speedup of the computation. Another advantage of this algorithm is the better scaling of the computation time as a function of the system size. The results of the application of this model to computing the self-organization process of the dynamics of carbon nanotubes are demonstrated.

Physical and geometric models of heterogeneous porous media are constructed with direct allowance for their microstructure. A method is worked out for calculating the probability distributions of the energy and momenta of radiation particles interacting with a material of a complex chemical composition. The distributions are used for detailed simulation of the scattering and absorption of radiation in complex heterogeneous materials. An approach is developed for the discrete description of the realistic geometry of porous heterogeneous media taking into account their structure at the microlevel. The approach includes an algorithm for constructing a detecting system for the statistical estimation of the radiation energy release during its propagation in an object. The results of model calculations on a hybrid computing cluster K-100 are presented.

The influence of electron-ion collisions on breaking cylindrical nonlinear plasma oscillations is studied. Numerical calculations by the particle method and an analytic analysis by the perturbation method in the weak nonlinearity regime show that, with an increasing collision frequency, the time needed to break plasma oscillations increases. The threshold value of the collision frequency is found exceeding which the density singularity does not arise. In this case, the maximum of the electron density formed outside the axis of the oscillations, the growth of which in the regime of rare collisions leads to the breaking effect, after some growth begins to decrease due to the damping of the oscillations.

Using a conservative numerical method, a flow of viscous heat-conducting gas in the diffusor part of a spatial axisymmetric nozzle with a slanting exit section and partially overlapped critical section is simulated. The computations are carried out in a wide variation range of the parameters affecting the behavior and structure of the flow. The effect of the critical section’s area and pressure in the confusor part on the flow parameters in the diffusor part of the nozzle, position of flow separation points, and longitudinal and cross-sectional forces acting on the internal part of the nozzle is investigated. The distributions of the flow parameters in the nozzle are reported. The computations are carried out using parallel algorithms implemented on a computer system with a cluster architecture.

The paper presents the results of the mathematically simulated evolution of a 3D diffusion-induced flow over a disk (with diameter d and thickness H = 0.76 d) immersed in a linearly density-stratified incompressible viscous fluid (described by a system of the Navier–Stokes equations in the Boussinesq approximation). The disk rests at the level of the neutral buoyancy (coinciding with its symmetry axis z) and disturbs the homogeneity of the background diffusion flux in the fluid forming a complex system of slow currents (internal gravitational waves). Over time, two thin horizontal convection cells are formed at the upper and lower parts of the disk stretching parallel to the z axis and adjacent to the base cell with thickness d/2. This work is the first to analyze in detail the fundamental mechanism for the formation of each new half-wave near the vertical axis x (passing through the center of the disk) during half the buoyancy period of the fluid T_b. This mechanism is based on gravitational instability. The emergence of this instability is first detected at 0.473T_b at a height of 3.9 d above the center of the disk. The same mechanism is also implemented over the place where the body moves in the horizontal direction. The 3D vortex structure of the flow is visualized by constructing the isosurfaces of the imaginary part of the complex-conjugate eigenvalues of the velocity gradient tensor. In mathematical simulation, we employed a numerical method SMIF that has proved itself over three decades with an explicit hybrid finite-difference scheme for the approximation of the convective terms of the equations (second-order approximation, monotonicity).