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: 10.18698/2309-3684-2014-1-6881

The authors developed the analytical formula for fast and accurate calculation of pressure on the surface of rotation bodies with arbitrary shape, which were flown by supersonic gas. The paper provides examples of applying the method for three-dimensional flows of gas.

Kotenev V., Sysenko V. Analytical formula with improved accuracy for calculating pressure distribution on the surface of convex, blunt rotation bodies of arbitrary shape. Маthematical Modeling and Coтputational Methods, 2014, №1 (1), pp. 68-81

doi: 10.18698/2309-3684-2022-2-7887

A new dependence for the enthalpy profile in the boundary layer model. A new analytical dependence is proposed for the enthalpy profile in the boundary layer, the use of which makes it possible to quickly and efficiently obtain the distribution of heat flux over the surface of blunted bodies

Котенев В.П., Тонких Е.Г. Новая зависимость профиля энтальпии в модели пограничного слоя. Математическое моделирование и численные методы, 2022, № 2, с. 80–89

doi: 10.18698/2309-3684-2015-3-5867

The article considers the problem of determining the pressure on the body surface streamlined by a gas flow with a small supersonic speed (M < 1,5).The economic algorithm for calculating the pressure on the part of the surface of blunt bodies of revolution is developed. Examples of flow calculations over spheres and ellipsoids with different semi-axes ratios are presented. Comparison with accurate numerical calculations shows the effectiveness of the proposed approach.

Kotenev V., Sysenko V. Calculation of the pressure when streamlining blunt bodies with small supersonic speeds. Маthematical Modeling and Coтputational Methods, 2015, №3 (7), pp. 58-67

doi: 10.18698/2309-3684-2023-2-9099

The simple analytical formula for calculation of laminar specific heat flow (divided by corresponding value at the critical point) brought to sphere surface streamlined by supersonic gas flow are received in this work. The analysis of the results shows that the use of the presented formula gives the values of the specific heat flow with greater accuracy than the known approximate formulas. The comparing of the relative heat flow with the accurate computational results of solving the Navier-Stokes equations also confirm the effectiveness of the presented method. It is proposed to formulate a special rule of local spheres for a quick evaluation of the specific heat flow on the surfaces of other blunted bodies with different generators in the future.

Котенев В.П., Сысенко В.А. Новая зависимость профиля энтальпии в модели пограничного слоя. Математическое моделирование и численные методы, 2023, № 2, с. 90–99

doi: 10.18698/2309-3684-2019-3-100112

The paper considers a method for applying the analytical dependence to calculate the pressure on the surface of blunted cones in a supersonic gas flow at an angle of attack, taking into account the discontinuity in the generatrix curvature. To generalize the dependence on the case of three-dimensional flow, the method of local surfaces was used. The pressure coefficient on the surface of spherical bluntness is calculated separately from the conical part according to known ratios [1, 2]. The results were compared with empirical data and the results of accurate calculations in a strict mathematical formulation. The scope of applicability of the method is determined. From the comparison it follows that using the analytical formula for the pressure distribution on the surface of a blunted cone in three-dimensional flows in applied problems of aerodynamics allows significant simplifying calculations while maintaining good accuracy of the results.

Котенев В.П., Пучков А.С., Сапожников Д.А., Тонких Е.Г. Метод локальных поверхностей для моделирования давления на затупленном конусе при пространственном обтекании. Математическое моделирование и численные методы. 2019. № 3. с. 100–112.

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: 10.18698/2309-3684-2016-3-3352

Modification of Pohlhausen method is developed. It allows for quick and effective heat transfer distribution over the blunt body surfaces. Calculations were done. Their results are described in comparison with the numerical solution of a problem within the framework of Navier — Stokes equations.

Kotenev V., Bulgakov V., Ozhgibisova Y. Modification of Pohlhausen method for calculating heat transfer on blunt bodies. Маthematical Modeling and Coтputational Methods, 2016, №3 (11), pp. 33-52

doi: 10.18698/2309-3684-2015-1-1730

The article discusses a method for constructing an aircraft geometric shape for computing the parameters of aerogasdynamic flow as well as a method of meshing near the model to simulate the flow within the Navier–Stokes equations in the thin layer approximation. The results of the flow simulation are given. The calculations were performed on a multiprocessor computer system.

Bratchev A., Dubrovina A., Kotenev V., Maksimov F., Shevelev Y. Problem solution of aerodynamic design using multiprocessor computers. Маthematical Modeling and Coтputational Methods, 2015, №1 (5), pp. 17-30

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