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Попов, Игорь Викторович

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Институт ядерной физики и технологий
Цель ИЯФиТ и стратегия развития - создание и развитие научно-образовательного центра мирового уровня в области ядерной физики и технологий, радиационного материаловедения, физики элементарных частиц, астрофизики и космофизики.
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Игорь Викторович
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2019 - 201922020 - 20212
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  • Уменьшенное изображение
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    Modeling Wave Processes in Elastic Media Based on Conservative Difference Schemes
    (2021) Popov, I. V.; Попов, Игорь Викторович
    © 2021, Pleiades Publishing, Ltd.Abstract: The problems of the numerical calculation of the propagation of deformations in elastic heat-conducting media are considered. To solve this class of problems, implicit numerical schemes are proposed for the equations of thermoelasticity and thermal conductivity on unstructured triangular and tetrahedral meshes. As a result of theoretical studies, it is shown that the proposed schemes have the properties of self-adjointness and sign-definiteness of difference operators, as well as conservatism. The results of the numerical experiments are also presented, confirming the effectiveness of the developed technique.
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    On Monotonic Finite Difference Schemes
    (2020) Popov, I. V.; Попов, Игорь Викторович
    © 2020, Pleiades Publishing, Ltd.Abstract: We propose an approach to construct monotonic finite difference schemes for solving the simplest elliptic and parabolic equations with the first derivatives and a small parameter at the highest derivative. For this, the notion of adaptive artificial viscosity is introduced. The adaptive artificial viscosity is used to construct monotonic difference schemes with the flow approximation of order O(h4 for the boundary layer problem and O(τ2+h2) for Burgers’ equation, where h and τ are mesh steps in space and time, respectively. The Samarskii–Golant approximation (or upwind difference schemes) is used outside the region of high gradients. The importance of using schemes of second-order accuracy in time is outlined. The computational results are presented.
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    Construction of Higher-Order Approximation Difference Scheme for Nonlinear Convection-Diffusion Equation Using Adaptive Artificial Viscosity in Case of Two-Phase Filtering Problems
    (2019) Popov, I. V.; Poveshchenko, Y. A.; Polyakov, S. V.; Попов, Игорь Викторович; Повещенко, Юрий Андреевич; Поляков, Сергей Владимирович
    © 2019, Springer Nature Switzerland AG.The method of adaptive artificial viscosity is used to model the process of one-dimensional nonlinear convection-diffusion equation. For this purpose, a finite difference scheme (FDS) of the second order of time and space approximation has been developed. The scheme was tested using a numerical solution of the problem on formation of a gradient catastrophe. The process of two-phase filtration was analyzed with the help of constructed FDS. Numerical calculations showed that the proposed method, and in this case reliably tracks the discontinuities of the solution.
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    Numerical simulation in problems with dissociation of gas hydrates in a porous medium in one-dimensional formulation
    (2019) Podryga, V. O.; Popov, S. B.; Rahimly, P. I.; Kazakevich, G. I.; Poveshchenko, Y. A.; Popov, I. V.; Повещенко, Юрий Андреевич; Попов, Игорь Викторович
    © 2019, Kazan Federal University. All rights reserved.The paper deals with some typical problems of gas hydrates dissociation in a porous medium, which in the first approximation can be reduced to one-dimensional. The research aims to study the mutual effects of underground gas hydrates and climate change, as well as some important technological and ecological problems of the flow in the well or fault area in the presence of hydrate-containing formations. New conservative difference schemes were developed for this class of problems. They are based on the splitting of gas-hydrodynamic processes. The advantage of these schemes is the phased solution of parabolic and hyperbolic equations. This approach greatly simplifies the solution procedure and at the same time increases its stability. Notably, within the framework of the approach, an algorithm was proposed to jointly solve the systems of equations describing the processes in various fields characterized by their own set of coexisting phases. The coordination of computational schemes for them is not a trivial and automatic process. Numerical calculations using mathematical modeling for the joint description of the gas hydrate zone and the zone with no gas hydrates were carried out. The results of calculations showed the applicability of the developed methods for solving the problems under study.