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8100
Секция 5
Список литературы
1. Толстых М. А., Желен Ж. Ф., Володин Е. М., Богословский Н. Н., Вильфанд Р. М., Киктев Д. Б., Красюк Т. В., Кострыкин С. В., Мизяк В. Г., Фадеев Р. Ю., Шашкин В. В., Шляева А. В., Эзау И. Н., Юрова А. Ю. Разработка многомасштабной версии глобальной модели атмосферы ПЛАВ // Метеорология и гидрология. 2015. № 6. С. 25-35.
2. Tolstykh, M., Shashkin, V., Fadeev, R., and Goyman, G.: Vorticity-divergence semi-Lagrangian global atmospheric model SL-AV20: dynamical core // Geosci. Model Dev. 2017. V 10. P. 1961-1983.
3. Толстых М. А., Шашкин В. В., Фадеев р. Ю., Шляева А. В., Мизяк В. Г., Рогутов В. С., Богословский Н. Н., Гойман Г. С., Махнорылова С. В., Юрова А. Ю. Система моделирования атмосферы для бесшовного прогноза. Рецензент д.ф-м.н. А. В.Старченко. М.: Триада лтд., 2017. 166 стр. ISBN 978-5-9908623-3-3.
Оценка загрязнения Малого моря (Байкал) с помощью численного моделирования
Е. А. Цветова
Институт вычислительной математики и математической геофизики СО РАН Email: e.tsvetova@ommgp.sscc.ru DOI: 10.24411/9999-017A-2020-10169
После закрытия Байкальского целлюлозного комбината в регионе не осталось промышленных предприятий, сбрасывающих загрязненные воды в озеро. Однако вместо одного крупного источника в настоящее время образовалось множество мелких - это объекты туристической отрасли. Одним из самых посещаемых мест на Байкале является остров Ольхон, который отделен от материка заливом Малое Море.
В докладе предпринята попытка оценить текущее состояние и возможные последствия загрязнения Малого Моря с помощью методов математического моделирования. С этой целью используется трехмерная негидростатическая модель гидротермодинамики и распространения примесей, которая рассматривается в локальной зоне с учетом влияния крупномасштабных процессов в озере. В условиях имеющейся неопределенности при задании источников воздействий и параметров математической модели для воспроизведения физических процессов в озере и получения оценок используется сценарный подход, позволяющий построить варианты развития ситуаций.
Работа выполнена в рамках бюджетного проекта ИВМиМГ СО РАН (№ 0315-2019-0004) в части разработки базовых моделей озера и при финансовой поддержке Российского фонда фундаментальных исследований (код проекта 20-01-00560) при решении задач продолжения.
A study of the nonlinear longitudinal oscillations in an elastic rod in the presence of the nonstationary source
Yu. A. Chirkunov
Novosibirsk State University of Architecture and Civil Engineering
Email: chr101@mail.ru
DOI: 10.24411/9999-017A-2020-10170
We found all basic models having different symmetry properties of the general model of the nonlinear longitudinal oscillations in an elastic rod in the presence of the nonstationary source. For a basic model that admits the widest group of Lie transformations, we obtained all invariant submodels. The solutions describing these submodels are found either explicitly, or their search is reduced to solving of the nonlinear integral equations. The presence of arbitrary constants in the integral equations describing invariant solutions of rank 1 allows us to study having physical meaning boundary value problems analytically and numerically. For the invariant submodels obtained, we studied nonlinear longitudinal oscillations of an elastic rod, for which either a longitudinal displacement and speed of its change or a longitudinal displacement and its gradient are specified at the initial moment of the time at a fixed point. We are established the existence and uniqueness of the solutions of these boundary value problems under some additional conditions. Their solution is reduced to the solution of the integral equations, which we solved numerically for some values of the included in them parameters.
The study was carried out with the financial support of RFBR and the Government of the Novosibirsk region in the framework of the Project № 19-41-540004.
Математические модели физики атмосферы, океана и окружающей среды 101
References
1. Yu. A. Chirkunov. Nonlinear longitudinal oscillations of viscoelastic rod in Kelvin model // J. Appl. Math. and Mech. 79. (2015). 506-513.
A study of the three-dimensional model of Khokhlov - Zabolotskaya - Kuznetsov nonlinear hydroacoustics in a cubically nonlinear medium, describing the nonlinear extinction of the ultrasonic beams in the presence of dissipation
Yu. A. Chirkunov
Novosibirsk State University of Architecture and Civil Engineering (Sibstrin)
Email: chr101@mail.ru
DOI: 10.24411/9999-017A-2020-10373
A generalization of the three-dimensional model Khokhlov-Zabolotskaya-Kuznetsov model in a cubically nonlinear medium with the special nonlinear coefficients describes an effect of attenuation of powerful ultrasonic beams due to the formation of shock waves. We got all invariant submodels of this model. The submodels of this model are described by the invariant solutions of the three-dimensional partial differential equation. We have studied all essentially distinct, not linked by means of the point transformations, invariant solutions of rank 0 and rank 1 of this equation. These solutions are found either explicitly, or their search is reduced to the solution of the nonlinear integro-differential equations. We researched the nonlinear attenuation of high-power ultrasonic acoustic waves (one-dimensional, axisymmetric and planar) for which the acoustic pressure, speed and acceleration of its change are specified at the initial moment of the time at a fixed point. Under the certain additional conditions, we established the existence and the uniqueness of the solutions of boundary value problems, describing these wave processes.
The study was carried out with the financial support of RFBR and the Government of the Novosibirsk region in the framework of the Project № 19-41-540004.
References
1. Rudenko O. V. On the 40th anniversary of the Khokhlov - Zabolotskaya equation. Acoustic. Phys. 2010. V. 56. No 4. P. 452-462.
Submodels of the three-dimensional model of Khokhlov - Zabolotskaya - Kuznetsov nonlinear hydroacoustics in a cubically nonlinear medium, describing an increasing pressure in ultrasonic beams due to inertialess self-focusing
Yu. A. Chirkunov
Novosibirsk State University of Architecture and Civil Engineering (Sibstrin)
Email: chr101@mail.ru
DOI: 10.24411/9999-017A-2020-10372
We got all invariant submodels of the generalization of the Khokhlov - Zabolotskaya - Kuznetsov model (3KZK) of nonlinear hydroacoustics in a cubic-nonlinear medium in the presence of dissipation. In particular, we obtained the submodels that we called by "Ultrasonic needles" that have the following property: at each fixed moment of the time in the field of the existence of the solutions, near some point, the pressure increases and becomes infinite in this point. Also we obtained the submodels that we called by "Ultrasonic knifes" that have the following property: at each fixed moment of the time in the field of the existence of the solution, near some plane the pressure increases and becomes infinite on this plane. The same as Ultrasonic needles, these submodels can be used, in particular, in medicine as a test in preparing for the operations with a help of an ultrasound. The presence of the arbitrary constants in the integro-differential equations, that determine invariant submodels of rank 1 provides a new opportunities for analytical and numerical study of the boundary value problems for the received submodels, and, thus, for the original (3KZK) model. We researched a propagation of the intensive acoustic waves (one-dimensional, axisymmetric and planar) for which the acoustic pressure, speed and acceleration of its change are specified at the initial moment of the time at a fixed point. Under the certain additional conditions, we established the existence and the uniqueness of the solutions of boundary value problems, describing these wave processes.
The study was carried out with the financial support of RFBR and the Government of the Novosibirsk region in the framework of the Project № 19-41-540004.
