Modeling of curved surfaces in gas dynamics problems

D. D. Zaripova ; Yu. M. Kovalev

Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, Tome 14 (2022) no. 2, pp. 59-63

Résumé

In this paper, a method for setting initial conditions on the boundary of an arbitrarily-shaped body on a rectangular grid is presented. A spherical volume of compressed gas, formed as a result of an explosion above the Earth's surface, is chosen as the body under consideration. Since the cells of the computational grid are rectangular and the contour is curvilinear, fractional cells are used to set the conditions on the boundary. The pressure and density inside the sphere are known and distributed uniformly throughout the volume. The parameters on the boundary are proposed to be calculated in proportion to the volume that the body takes in each cell the contour crosses. Such a volume can be found by integrating over the region cut off by the curve from a rectangular grid cell. The algorithm has been tested on a numerical solution to the problem of the gas sphere expansion by the large-particle method. Since the boundary of the sphere is a contact discontinuity, graphs of the position of density isolines in the process of expansion of the sphere are presented. The calculation results have shown that the described mechanism ensures the preservation of the spherical boundary during the calculation process: the deviation from the values corresponding with the circle equation has equaled less than 1%.

Détail

Keywords: mathematical modeling, gas dynamics, boundary conditions, fractional cells.