The modeling of two-dimensional vortex flows in a cylindrical channel using parallel calculations on a supercomputer

Abstract

Objectives . The study aimed to examine vortex structures formed during the interaction of incident and reflected shock waves in a cylindrical channel. The shock wave was described by the Hugoniot relations, which make it possible to determine the parameters of the gas behind the shock front by a given Mach number and the values of the gasdynamic parameters ahead of the pressure jump. The propagation of a strong shock wave (Mach number was 20) in argon was simulated. Methods . The methods of mathematical modeling were used. A parallel algorithm for solving two-dimensional equations of gas dynamics in cylindrical coordinates (r, z, t) was developed and a new version of the NUTCY_ps program created. The calculations were performed on an MVS-100K supercomputer. Results. Two methods of parallelization when solving a system of equations were considered. Using a specific task as an example, a comparison of the effectiveness of these methods was conducted. A parallel algorithm was developed and a program was upgraded for solving two-dimensional equations of gas dynamics in cylindrical coordinates (r, z are spatial coordinates, t is time). Numerical calculations were performed to simulate: 1) the shock wave incidence to and reflection from a metal screen; 2) the propagation of the shock wave through a hole in the screen; 3) the propagation of the shock wave through a cylindrical channel and its reflection from the bottom of the channel and interaction with the incident wave. The results obtained by the parallel supercomputer with different numbers of processors are presented. It is shown that using 16 processors, it is possible to reduce the computation time for getting a solution for the test problem by approximately 12 times. Conclusions . It is shown that the interaction of incident shock wave and the one reflected at an angle leads to the formation of regions with low and high gas densities, as well as vortex flows. The vortex interaction area (turbulence zone) gets a complex shape. The article discusses the possibility of carrying out full-scale experiments in shock tubes or using a laser shock tube. Such studies would make it possible to compare experimental data with the results of numerical simulation and, on their basis, to develop more advanced models of turbulent motions.