Персона: Шильников, Кирилл Евгеньевич
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Институт лазерных и плазменных технологий
Стратегическая цель Института ЛаПлаз – стать ведущей научной школой и ядром развития инноваций по лазерным, плазменным, радиационным и ускорительным технологиям, с уникальными образовательными программами, востребованными на российском и мировом рынке образовательных услуг.
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Кирилл Евгеньевич
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- ПубликацияТолько метаданныеNumerical simulation of cryosurgery in biological tissue with developed circulatory system(2019) Shilnikov, K. E.; Kochanov, M. B.; Шильников, Кирилл Евгеньевич; Кочанов, Марк Борисович© Published under licence by IOP Publishing Ltd.This paper is devoted to the modeling of the cryogenic impact on biological tissue with a developed circulatory system: large blood vessels, dense distributed small vessels and capillaries penetrating the tissue. The case of cryogenic destruction of a cancer tumor localized near a large artery is considered. The paper presents a direct numerical simulation of the temperature distribution evolution in biological tissue including the calculation of blood flow parameters in a vessel. The mathematical model is based on the Pennes bioheat transfer model with enthalpy modification and the quasi-one-dimensional hemodynamic model of blood flow in arteries, taking into account local changes in the elastic properties of the vessel walls due to strong cooling of adjacent tissue. A numerical algorithm based on explicit finite-volume approximation of the heat transfer model and the hybrid characteristic scheme (after splitting the equation with respect to physical processes) for numerical solution of hyperbolic systems is developed in order to simulate cryosurgery for the tumor near the artery. The main focus of the paper is a numerical study of the circulatory system parameters' influence on the shape of the final distribution of the cellular necrosis zone. We study the dependence of the necrosis front penetration depth on the perfusion power which characterizes the density of capillary distribution, the peak and background rates of blood flow in the artery, the diameter of the blood vessel and the thickness of its walls.
- ПубликацияТолько метаданныеOn one approach for the numerical solving of hyperbolic initial-boundary problems on an adaptive moving grids(2023) Shilnikov, K. E.; Kochanov, M. B.; Шильников, Кирилл Евгеньевич; Кочанов, Марк БорисовичAn approach for the quality improvement of numerical modeling of the processes described by nonlinear hyperbolic equations, which have conservative form is proposed. The transition to synchronous moving coordinate system along with Godunov type numerical scheme for the problem on moving mesh is applied. The grid motion law relies heavily on Rankine–Hugoniot relations. In order to prevent the degeneration of moving computational mesh the regularization mechanism is implemented. It allows to almost automatically fit the computational mesh to the admissible width of the solution singularity resolution. The proposed algorithm is tested on several initial-boundary problems for the Hopf equation with well known exact solutions. The hyperbolic Buckley–Leverett equation is also considered as an example of application of the proposed approach. © 2022 Elsevier B.V.
- ПубликацияТолько метаданныеExploring the Efficiency of Neural Networks for Solving Dynamic Process Problems: The Fisher Equation Investigation(2024) Karachurin, R.; Ladygin, S.; Ryabov, P.; Shilnikov, K.; Kudryashov, N.; Карачурин, Рауль Нуриевич; Ладыгин, Станислав Аркадьевич; Рябов, Павел Николаевич; Шильников, Кирилл Евгеньевич; Кудряшов, Николай Алексеевич