卷 9, 编号 6 (2017)

The error in approximating a Cauchy problem for a two-dimensional wave equation based on a scheme with weights is studied. The dependence of the approximation error on the time step and weight parameter is considered. With this aim in view, the difference of second-order spatial derivatives in the wave equation is approximated, while the time derivative is preserved continuous; and an analytical solution of a Cauchy problem for a system of ordinary differential equations is obtained as the decomposition in the orthonormal basis consisting of the eigenvectors of the operator of the second difference derivative with respect to the spatial variables. Based on this solution, the errors of the approximation of the wave problem by three-layer difference schemes are studied and the conditions for the stability of a three-layer difference scheme are obtained. It is established that, when simulating the propagation of oscillation processes using difference methods, the oscillation frequency values differ from the real ones and depend on the weight parameter and time step. The optimal values of the weight parameter with which the deviation of the oscillation frequency for the difference scheme is minimal are obtained. The dependences of the approximation error on weight and spatial step are derived. The optimal values of the weight parameter with which the schemes are of the second and fourth order of accuracy with respect to the time step are found.

An approximate method is developed for calculating the instability boundaries, as well as the frequencies and amplitudes, of acoolant’s autooscillations self-excited during its motion in a vertical channel exposed to locally applied heat from a constant power source. Unlike in the classical generators of thermoacoustic oscillations such as the Rijke tube and Lehmann’s plant, it is assumed that the main stationary flow is collinear with the gravity force. In order to exclude the surging nature of the self-oscillations, it is assumed that the flow is created by a supercharger with a monotonically decreasing head-capacity characteristic. The resulting mathematical model makes it possible to theoretically determine the self-excitation conditions of the considered autooscillations and also to evaluate the effect of various parameters on their shape.

This paper is devoted to the development of computational techniques for simulating low Mach number flows on unstructured meshes based on the Roe method and the edge-based vertexcentered higher accuracy schemes. The techniques are implemented in the in-house NOISEtte code. The results of predicting an inviscid compressible low Mach number flow over a NACA0012 airfoil are presented and analyzed. The computations are carried out on structured and unstructured triangular grids.

Modeling the global distribution of the electric potential in the Earth’s ionosphere is based on the solution of a 2D continuity equation in the ionospheric-magnetospheric current circuit. The potential distribution is described by the boundary value problem for an elliptic system of partial differential equations on the spherical shell approximating the ionosphere, which is divided into three subregions with nonlocal boundary conditions. Implementation of the boundary conditions, which reflect the continuity of the common current circuit and potential equalization at the boundaries of the polar caps, is leading to the mutual dependence of the potential distribution within the northern and southern caps and their influence on the potential distribution in the midlatitude region. The problem is solved by an iterative method with a regularizing operator which is inverted using the separation of the variables and the fast Fourier transform with respect to the azimuthal variable and the sweep method with respect to the latitudinal one.

The goal of this work is to study the applicability of modern GPUs for the computation of combustion and detonation problems for a nonstationary regime. The capacity of the graphics card and universal processors connected in parallel for solving problems of detonation initiation is compared.

The reconstruction problem is studied for a current pulse passing through a hollow cylindrical conductor (tube) such that the wall thickness is much greater than the thickness of the skin layer. The time dependence of the electric field intensity measured on the inner surface of the tube is used to reconstruct the current pulse. The proposed method allows us to study the evolution of the penetration of the magnetic field through the conductor thickness. The results for the test problems (both for the case of a constant temperature and for the case where the temperature varies over the tube thickness) are presented. Also, the current pulse is reconstructed via the electric field intensity measured at the inner surface of the tube within the experiment executed on the Angara-5-1 installation.