Marchevskii

pp. 329-345

pp. 234-249

In this paper the authors consider a fast numerical algorithm for calculating convective velocities in the vortex element method. This algorithm is based on derivation of a tree of rectangular regions which contain vortex elements. Influence of parameters of the fast method on computational complexity of the algorithm was analyzed. The number of arithmetic operations required for calculating velocities of all vortex elements was evaluated for modeling an evolution of vortex motion in an ideal incompressible liquid. This theoretical estimation is in good agreement with the results of the numerical experiment. The developed approach could be useful in practice because it allows to select optimal values of the algorithm parameters a priori.

The Blasius benchmark problem dedicated to numerical simulation of a flow around a thin plate is considered in this paper. The laminar boundary layer was simulated using a modified numerical scheme of the vortex element method with tangent velocity components. This numerical scheme was implemented in POLARA software. Distributions of longitudinal and transversal velocity components over the boundary layer’s cross-section were obtained. Use of the modified scheme allowed to improve accuracy of determining the intensity of a vortex layer on the plate significantly at every step of the calculation. The obtained results appeared to be in good agreement with the analytic solution given by Blasius.