This article deals with the finite-element RKDG method (Runge-Kutta Discontinuous Galerkin) and its application for numerical integration of three-dimensional system of equations of ideal gas on unstructured grids. By means of the described algorithm we solved two test tasks. For each task we conducted the analysis and compared the task solution with well-known analytical solutions or with tabular data. We also give error assessment in the solution.
Dimitrienko Y., Koryakov M., Zakharov A. Application of RKDG method for computational solution of three-dimensional gas-dynamic equations with non-structured grids. Маthematical Modeling and Coтputational Methods, 2015, №4 (8), pp. 75-91
In the article we propose an algorithm for the numerical simulation of conjugate gasdynamic and thermomechanical processes in composite structures of high-speed aircraft. The algorithm allows calculating all parameters of the three-dimensional gasdynamic flow near the surface of the aircraft, heat exchange on the surface, heat and mass transfer processes in the internal structure of thermodestructive polymer composite, as well as processes of composite construction thermodeformation, including the effects of changes in the elastic characteristics of the composite, variable thermal deformation, shrinkage caused by thermal degradation, building up interstitial gas pressure in the composite. An example of numerical simulation of conjugated processes in a model composite construction of high-speed aircraft illustrates the possibilities of the proposed algorithm.
Dimitrienko Y., Koryakov M., Zakharov A., Stroganov A. Computational modeling of conjugated gasdynamic and thermomechanical processes in composite structures of high speed aircraft. Маthematical Modeling and Coтputational Methods, 2014, №3 (3), pp. 3-24
A coupled problem of high-speed aerothermodynamics and internal heat and mass transfer in heat-shielding structures of reentry spacecraft made of ablative polymer composite materials is considered. To determine the heat fluxes in the shock layer of the reentry vehicle, the chemical composition of the atmosphere is taken into account. The mathematical formulation of the conjugate problem is formulated and an algorithm for the numerical solution is proposed. An example of the numerical solution of the problem for the reentry spacecraft Stardust is presented. It is shown that taking into account chemical reactions in the gas flow around the surface of the reentry vehicle is essential for the correct determination of the gas temperature in the boundary layer. It is also shown that the developed numerical method for solving the problem makes it possible to determine the parameters of phase transformations in a heat-shielding structure depending on the heating time, in particular, it allows calculating the pore pressure field of gaseous products of thermal decomposition of a polymer composite, which, under certain conditions, can lead to material destruction.
мДимитриенко Ю.И., Коряков М.Н., Юрин Ю.В., Захаров А.А., Сборщиков С.В., Богданов И.О. Сопряженное моделирование высокоскоростной аэротермодинамики и внутреннего тепломассопереноса в композитных аэрокосмических конструкциях. Математическое моделирование и численные методы, 2021, № 3, с. 42–61.
The problem of developing a model for calculating temperature fields in thin-walled multilayer curvilinear-anisotropic thin shells of arbitrary geometric shape, including composite ones, is considered. As a rule, to solve this problem, a specific coordinate notation of the equations of the theory of heat conduction is used, which creates certain difficulties for calculating complex composite shells. In this paper, it is proposed to use an invariant record of the variational formulation of problems in the theory of heat conduction, followed by the application of the finite element algorithm procedure. As a result, a matrix differential equation is derived for determining the temperature field at the nodes of a finite element mesh. A software module has been developed for the finite element solution of the problem of non-stationary thermal conductivity of shells. The module functions as part of the SMCM software package, created at the Scientific and Educational Center for Supercomputer Engineering Modeling and Development of Software Systems, Bauman Moscow State Technical University (REC SIMPLEX). An example of solving the problem of calculating a non-stationary temperature field in a cylindrical shell with longitudinal-transverse reinforcement is given. Comparison of numerical simulation with similar calculations in the ANSYS software was carried out, which showed the high accuracy of the proposed method: the relative deviation of the results does not exceed 0,5%
Димитриенко Ю.И., Юрин Ю.В., Коряков М.Н., Маремшаова А.В. Конечно-элементное моделирование температурных полей в тонкостенных многослойных оболочечных элементах конструкций. Математическое моделирование и численные методы, 2023, No 1, с. 43–63
The coupled task of aero-thermo-mechanics of heat-loaded structures from thermally destructive polymer composite materials under the influence of an intense aerodynamic flow is considered. The mathematical formulation of the conjugate problem is formulated and algorithms for the numerical solution of this problem are proposed. The algorithms are based on an iterative solution of three types of problems: aerodynamics, internal heat and mass transfer, and thermomechanics of the modeling aircraft structure. An example of a numerical solution to the problem for an aircraft structural element in the form of a blunt cone is presented. It is shown that the effect of high temperatures of aerodynamic heating of the structure leads to thermal degradation of the polymer composite material, which results in the generation of a large amount of gases in the pores and thermo-chemical shrinkage, which under certain conditions can lead to premature destruction of the heat-loaded composite structure.
Димитриенко Ю.И., Коряков М.Н., Юрин Ю.В., Захаров А.А. Конечно-элементное моделирование термонапряжений в композитных термодеструктирующих конструкциях при аэродинамическом нагреве. Математическое моделирование и численные методы, 2019, № 2, с. 15–34.