and Computational Methods

doi: 10.18698/2309-3684-2017-3-83104

The study introduces an algorithm for classifying the aircraft surface elements based on a binary decision tree with threshold predicates. According to the initial description of the objects, we developed derived characteristics allowing for the classes to be separated with minimal losses. Moreover, we trained and verified the predicates on synthetic data and described an algorithm of obtaining the data for training. Low values of classification errors and ease of implementation make it possible to apply the algorithm for solving aerodynamic applied problems.

Kotenov V.P. ,Ratslav R.A. ,Sapozhnikov D.A. ,Chernyshev I.V. , A method for classifying aircraft surface elements for the numerical-analytical solution of aerodynamic problems .Маthematical Modeling and Computational Methods, 2017, №3 (15), pp. 83–104

doi: 10.18698/2309-3684-2017-2-8193

The article presents an analytical expression for calculating pressure on the surface of blunted cones in a supersonic gas flow, taking into account the curvature discontinuity along the generatrix. We used a genetic algorithm and multi-stage functional optimisation methods for the least-squares method to determine free parameters of the expression. We compare the results obtained to the rigorous numerical solution to the inviscid problem. The comparison shows that it is possible to use the analytical expression for pressure distribution over a surface in a wide Mach number range for various cone halfangles. The expression proposed accounts for the curvature discontinuity along the generatrix at the point where the sphere is tangent to the conical surface, unlike the expressions found in previously published works.

Bulgakov V.N., Kotenev V.P., Sapozhnikov D.A. Modeling supersonic flow around blunted cones, taking into account the curvature discontinuity along the generatrix of the solid. Маthematical Modeling and Coтputational Methods, 2017, №2 (14), pp. 81-93

doi: 10.18698/2309-3684-2017-4-6072

The article introduces a dependency for the pressure distribution in the disturbed region near the sphere streamlined by the flow of the supersonic inviscid gas, obtained when modifying the Shepard’s Method. We use known ratios for the pressure on the body and the shockwave as well as data from the numerical experiments. We have compared the results with the data not used in the learning process of the dependency coefficients. This comparison proves high confidence of the model obtained.

Kotenev V.P., Puchkov A.S., Sapozhnikov D.A., Tonkikh E.G. Simulation of the pressure distribution in the disturbed region near the sphere streamlined by the inviscid flotation by means of the machine learning methods. Mathematical Modeling and Computational Methods, 2017, №4 (16), pp. 60-72

doi: 10.18698/2309-3684-2018-2-109121

The generalization of the dependency which was proposed earlier for determining of the pressure in perturbed area streamlined by the supersonic flow of the inviscid perfect gas was provided. The modification allows to consider effects which occur when the sphere is streamlined by high temperature gas with adiabatic index which do not equal 1.4. According to article [2-3], made adjustment to the function which describes the behavior of the shock wave which depends on the adiabatic index. The Shepard function’s coefficient also consider of adiabatic index. First and second order members of Shepard function which describe a pressure in area does not change. Comparison of application versions with the available data calculations for the high temperature gas and approximations based on perfect gas shows high accuracy of the proposed approach.

Котенев В.П., Пучков А.С., Сапожников Д.А., Тонких Е.Г. Восстановление распределения давления в возмущенной области около сферы, обтекаемой сверхзвуковым потоком газа с произвольным эффективным показателем адиабаты. Математическое моделирование и численные методы, 2018, № 2, с. 109–121