РАЦИОНАЛИЗАЦИЯ АЛГОРИТМА МОДЕЛИРОВАНИЯ ПОВЕРХНОСТИ МЕТОДОМ БРОУНОВСКОГО ДВИЖЕНИЯ ПО КРИТЕРИЮ МИНИМИЗАЦИИ КОЛИЧЕСТВА ИТЕРАЦИЙ

Abstract

The paper has been devoted to construction of geometric model for real surface’s compartment at micro- and nanoscales with known fractal dimension. Receiving data on the real surface’s fractal dimension has been considered in [8; 9; 11; 13; 20]. Fractal dimension as a relief development measure has been accepted for the necessary and sufficient condition of the model construction. As is known, for a flying vehicle’s appearance the comprehensive characteristics research is performed with ground work in aerodynamic tubes, and numerical simulation. Similarly, a fragment of product’s heat protection is tested in high-enthalpy facilities for research of physico-chemical processes in the boundary layer, as well as for confirmation of calculations of interactions between rarefied gas’s particles and the surface. In this work has been performed the analysis of geometrical interpretations of algorithms for the fractal surfaces formation based on the Brownian motion method, proposed to use in calculations by Monte Carlo and Navier-Stokes methods. A point choice leading to construction of secant or tangent planes to space forms has been assigned as an element of randomness per iteration. All proposed algorithms lead to construction of surfaces with fractal dimension D ≈ 2.5, but by different iterations number. A tendency to reduce the iterations number required to achieve a specific fractal dimension by increasing the capacity of many lines for plane compartment digitalization has been revealed. The best result has been obtained by construction of projections for section of surface called a torus knot [19, 22]. Visualization was carried out in ASCON Kompas 3Dv.14 program on algorithms results in MathCAD environment.