and Computational Methods

doi: 10.18698/2309-3684-2023-4-2746

The results of numerical simulation of two-dimensional plane laminar flows near two inclined plates forming a constricting nozzle along the velocity vector of an incoming supersonic perfect gas flow are presented. A multi-block computational technology is applied with the use of local curvilinear grids adapted to the surface of bodies, which have finite areas of overlap with a global rectangular grid for the entire computational domain. Viscous boundary layers are resolved on local grids using the Navier-Stokes equations, and the effects of aerodynamic interference of accompanying shock-wave structures are described in terms of the Euler equations. In areas of grid overlap, function interpolation is applied up to the boundaries of the transition from one grid to another. With a successive increase or decrease in the Mach number of the oncoming supersonic flow, a qualitative rearrangement of the flow structure near the nozzle is detected - either a detached shock wave and a subsonic flow zone in front of the nozzle, or oblique shocks near inclined plates are formed. A hysteresis is revealed, which is expressed in the fact that in a certain range of Mach numbers, the flow structure and the aerodynamic load on the nozzle depend not only on the value, but also on the prehistory of the change in the Mach number. The possibility of changing the flow structure by introducing a density inhomogeneity into the oncoming flow is shown.

Максимов Ф.А. Численное моделирование гистерезиса при обтекании плоского сопла. Математическое моделирование и численные методы, 2023, № 4,с. 27–46.

doi: 10.18698/2309-3684-2015-1-1730

The article discusses a method for constructing an aircraft geometric shape for computing the parameters of aerogasdynamic flow as well as a method of meshing near the model to simulate the flow within the Navier–Stokes equations in the thin layer approximation. The results of the flow simulation are given. The calculations were performed on a multiprocessor computer system.

Bratchev A., Dubrovina A., Kotenev V., Maksimov F., Shevelev Y. Problem solution of aerodynamic design using multiprocessor computers. Маthematical Modeling and Coтputational Methods, 2015, №1 (5), pp. 17-30

doi: 10.18698/2309-3684-2015-1-109120

The supersonic flows are implemented in an axisymmetric channel in many technical devices. These flows are in an expanding part of the nozzle or in the working part of supersonic wind tunnel. The method of supersonic flow calculation in an axisymmetric channel is developed. The method is based on the construction of multi-block axisymmetric grid and linearization of boundary conditions on the aerodynamic surfaces. Testing the method has showed good agreement with known experimental data. The method allows predicting the aerodynamic properties of the aerodynamic form, depending on its location in the channel, as well as the effect of the aerodynamic form on the channel walls in the channel.

Maksimov F. Supersonic flow in axisymmetric channel. Маthematical Modeling and Coтputational Methods, 2015, №1 (5), pp. 109-120