Vol 8, No 5 (2016)

Using a simple model of a linear transfer equation, a family of hybrid monotonic finite-difference schemes is constructed. By differential approximation analysis, it is shown that the resulting family yields a second-order approximation in the spatial variable, having minimal scheme viscosity and dispersion and being monotonic. It is demonstrated that the operability domain of the basic schemes, namely, the modified central difference schemes (MCDS) and the modified upwind difference schemes (MUDS), forms a nonempty set. A local criterion for switching between the basic schemes is proposed; this criterion employs the sign of the product of the velocity, as well as the first and second differences of the transferred functions at the considered point. Within the studied schemes, the optimal pair of basic schemes, possessing the above-mentioned properties and being closest to the third-order scheme, is obtained. On the solution of the Cauchy problem, the calculation results obtained using some well-known first-, second-, and third-order schemes are compared graphically.

The phenomena of the movement and destruction of celestial bodies in the Earth’s atmosphere are investigated based on the advanced equations of meteor physics. The movement of meteorites in Kunya-Urgench (1998) and Chelyabinsk (2013) is analyzed as an example taking into account changes in the ablation along the trajectory. Different mechanisms of destruction of these meteorites are described.

Various criteria of multiaxial fatigue fracture are studied for low-cycle fatigue (LCF); their generalizations are proposed for a very-high-cycle fatigue (VHCF) regime. The procedure of the stress state calculation is described for the compressor disk of the gas-turbine engine (GTE) in the flight cycle of loading and for the low-amplitude vibrations of the blades. The durability estimations of the disk operation are obtained for alternative mechanisms of LCF and VHCF using the calculated stress state and the models of multiaxial fatigue fracture. The results are compared with the data observed during operations.

The classical Godunov scheme for the numerical solution of 3D gas dynamics equations is justified in the multidimensional case. An estimate is obtained for the error induced by replacing the exact solution of the multidimensional discontinuity breakup problem (known as the Riemann problem) with the solution of the 1D problems with the data on the left and right of the interface of each cell without considering the complicated flow in the neighborhood of the cells’ vertices. It is shown that, in the case of plane interfaces, the error has the first order of smallness in the time step and the approximate solution converges to the solution of semidiscrete equations as the time step vanishes. In fact, the time integration of these equations using the explicit Euler method represents the Godunov scheme.

This paper presents the numerical simulation of the circumfluence of a recovery apparatus with brake engines and a detachable heat protection shield carried out by the use of the conservative numerical method of cluster architecture. The simulation results of the action of reactive jets of brake engines on the landing surface and the recovery apparatus, as well as the basic aerodynamic characteristics, are considered.

The work is dedicated to the numerical investigation of different propagation regimes of a gaseous pulsating detonation wave using two approaches. In the first one, the problem is solved in the laboratory frame and the detonation is initiated near the closed end of the channel. In the second approach, the simulation is carried out in the shock-attached frame. For this purpose, a second approximation order algorithm for the integration of the shock evolution equation using the grid-characteristic method is proposed. The stable, weakly unstable, and irregular regimes of detonation wave propagation are investigated using both approaches. The qualitative and quantitative differences between the two approaches are put forward.