ALGORITHMS FOR CONTROL ENFORCEMENT OF THE IMPERMEABILITY CONDITION FOR THE METHOD OF DISCRETE SINGULARITIES

Abstract

A system of algorithms is presented for determining the position of the marked particle within the band of the boundary element, with subsequent correction of its position (taking into account the requirements of the mathematical model of the problem). The algorithm for finding the closest point on the boundary contour, at a distance of no more than a given value, for the sought point is presented. Individual cases arising from the interaction of different boundary elements or when the position of a marked particle changes through the boundary contour by a distance twice the thickness of the boundary element is considered. According to the logic of the construction of the above algorithms, the above algorithms have a better speed estimate than the full search algorithm. The memory limitation of existing computers requires an increase in the efficiency of data processing algorithms for the formation and preservation of sparse matrices. The improvement in the estimate of amount of used memory is due to the increase in the speed estimate, which is in its turn due to the increase in the number of operations required to find the desired element in the matrix. A number of different methods aimed at improving the performance estimates are presented. The system of algorithms for impermeability control during the interaction of impermeable moving free boundaries with impermeable fixed boundaries is intended for the improvement of discretized mathematical models of detachment aerodynamic processes in region with a boundary of complex geometry.