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Об условиях слабой консервативности некоторых явных разностных схем для уравнений одномерной баротропной газовой динамики
С. 37–38.
In book
М.: МИЭМ НИУ ВШЭ, 2017.
Zlotnik A., Lomonosov T., Математическое моделирование 2025 Т. 37 № 1 С. 151–170
A system of four balance differential equations is used to describe dynamics of heterogeneous compressible binary mixtures with stiffened gas equations of state for mixture components, including gas and liquid ones. The main points are its quasi-homogeneous form that arises as a result of eliminating volume fractions of components from the collection of sought functions ...
Added: October 6, 2024
Zlotnik A., Lomonosov T., Doklady Mathematics 2023 Vol. 108 No. 3 P. 443–449
We consider the so-called four-equation model for dynamics of the heterogeneous compressible binary mixtures with the Noble-Abel stiffened-gas equations of state. We exploit its quasi-homogeneous form that arises after excluding the volume concentrations from the sought functions and is based on a quadratic equation for the common pressure of the components. We present new properties ...
Added: March 1, 2024
А. А. Злотник, Т. А. Ломоносов, Доклады Российской академии наук. Математика, информатика, процессы управления (ранее - Доклады Академии Наук. Математика) 2023 Т. 514 № 1 С. 26–33
Рассматривается так называемая модель из четырех уравнений динамики гетерогенных сжимаемых бинарных смесей при уравнениях состояния “сжатого” газа Ноубла-Абеля. Используется ее квазигомогенная форма, возникающая после исключения объемных концентраций из искомых функций и основанная на квадратном уравнении для общего давления компонент. Приводятся новые свойства этого уравнения и простая формула для квадрата скорости звука, предлагается альтернативный вывод формулы, ...
Added: December 23, 2023
Zlotnik A., Applied Mathematics Letters 2023 Vol. 146 Article 108801
We deal with the so-called four-equation model for dynamics of the heterogeneous binary mixtures of the Noble-Abel stiffened-gases (NASGes). In relation to the quasi-homogeneous form of the model, we suggest a new insight on a quadratic equation for the pressure, give a simple formula for the squared speed of sound and present a new proof ...
Added: August 4, 2023
I. A. Kondratyev, S. G. Moiseenko, Lobachevskii Journal of Mathematics 2023 Vol. 44 No. 1 P. 44–56
In astrophysical fluid dynamics, some types of flows, like e.g., magnetorotational super- nova explosions, deal with a highly variable Mach number (from M ≪ 1 in the protoneutron star region to M ≫ 1 near the shock wave expelling from the stellar envelope) in presence of a strong differential rotation. The Courant–Friedrichs–Lewy (CFL) stability condition ...
Added: May 22, 2023
Fedchenko A., Journal of Mathematical Sciences 2023 Vol. 270 No. 6 P. 815–826
We consider regularizations of systems of equations for a multicomponent gas mixture dynamics in the barotropic multi-velocity and one-velocity cases. Energy balance equations are derived for them.
For the system of equations in the one-velocity case, the system linearized on a constant solution is studied, and, for the weak solutions to the initial-boundary value problem with ...
Added: May 11, 2023
Zlotnik A.A., Doklady Mathematics 2022 Vol. 106 No. 1 P. 236–242
We study an explicit two-level finite-difference scheme for a linearized multidimensional quasigasdynamic system of equations. For an initial-boundary value problem on a nonuniform rectangular mesh,
sufficient conditions of Courant-type for L^2-dissipativity are derived for the first time by applying the energy
method. For the Cauchy problem on a uniform mesh, both necessary and sufficient conditions for L^2-dissipativity ...
Added: September 7, 2022
А. А. Злотник, Доклады Российской академии наук. Математика, информатика, процессы управления (ранее - Доклады Академии Наук. Математика) 2022 Т. 505 № 1 С. 30–36
Изучается явная двухслойная разностная схема для линеаризованной многомерной квазигазодинамической системы уравнений. Для начально-краевой задачи на неравномерной прямоугольной сетке впервые даются достаточные условия $L^2$-диссипативности типа Куранта энергетическим методом. Для задачи Коши на равномерной сетке усовершенствуются как необходимые, так и достаточные условия $L^2$-диссипативности в спектральном методе. Указывается новая форма задания параметра релаксации, гарантирующая равномерную ограниченность сверху и снизу числа ...
Added: June 20, 2022
Zlotnik A.A., Lomonosov T.A., Mathematical Models and Computer Simulations 2021 Vol. 13 No. 6 P. 1097–1108
Explicit two-level difference schemes on staggered meshes are studied for two well-known
regularizations of 1D barotropic gas dynamics equtions, including schemes with discretization in
x with the property of total energy dissipation. The criteria of L^2-dissipativity in the Cauchy problem
are derived for their linearizations on a constant solution with zero background velocity. The criteria for
schemes on nonstaggered and staggered ...
Added: September 21, 2021
Afanaseva L., Bashtova E., Grishunina S., , in: Methodology and Computing in Applied ProbabilityVol. 22: Methodology and Computing in Applied Probability. Issue 4: Methodology and Computing in Applied Probability.: Netherlands: Springer, 2020. Ch. 3 P. 1439–1455.
We study the stability conditions of the multiserver system in which each customer requires a random number of servers simultaneously. The input flow is supposed to be a regenerative one and a random service time is identical at all occupied servers. The service time has an exponential or a phase-type distribution. We de fine an auxiliary ...
Added: February 2, 2021
Zlotnik A., , in: Differential and Difference Equations with Applications. ICDDEA 2019, Lisbon, Portugal, July 1–5Vol. 333.: Springer, 2020. P. 53–67.
We study an explicit two-level in time and three-point symmetric in space finite-difference scheme for 1D barotropic and full gas dynamics systems of equations. The scheme is a linearization at a constant background solution (with an arbitrary velocity) of finite-difference schemes with general viscous regularization. We enlarge recently proved sufficient conditions (on the Courant-like number) for $L^2$-dissipativity in ...
Added: November 1, 2020
Lomonosov T., В кн.: Межвузовская научно-техническая конференция студентов, аспирантов и молодых специалистов им. Е.В. Арменского.: М.: МИЭМ НИУ ВШЭ, 2019.
В работе приводятся критерии (необходимые и достаточные условия) $L^2$-устойчивости для линеаризованных на постоянном решении разностных схем, основанных на некоторой регуляризации 1D баротропных и полных уравнений газовой динамики. Техника вывода основана на спектральном подходе. ...
Added: December 11, 2019
Акимов В. С., Силаев Д. П., Симонов А. С. et al., Вычислительные методы и программирование: новые вычислительные технологии 2017 Т. 18 С. 406–415
The scalability of computations in FlowVision CFD software on the Angara-C1 cluster equipped with Angara interconnect is studied. Several test problems with 260 thousand, 5.5 million and 26.8 million computational cells are considered. Computations in FlowVision are performed using a new solver of linear systems based on the algebraic multigrid (AMG) method. It is shown ...
Added: October 30, 2019
Krasnobaev K. V., Fedchenko A., Journal of Physics: Conference Series 2018 No. 1129 P. 012012
The properties of interstellar gas produce significant effect on dynamic phenomena which occur at large heliocentric distances. HII region is a vivid example of the objects with extremely high radiation, where atoms of hydrogen are heated and ionized by ultraviolet radiation. This article deals with the HII region expansion. To study this process researches need ...
Added: October 13, 2019
Zlotnik A., Lomonosov T., Mathematical Modelling and Analysis 2019 Vol. 24 No. 2 P. 179–194
An entropy dissipative spatial discretization has recently been constructed for the multidimensional gas dynamics equations based on their preliminary parabolic quasi-gasdynamic (QGD) regularization. In this paper, an explicit finite-difference scheme with such a discretization is verified on several versions of the 1D Riemann problem, both well-known in the literature and new. The scheme is compared with the ...
Added: November 28, 2018
Balashov V., Savenkov E., Zlotnik A., Russian Journal on Numerical Analysis and Mathematical Modelling 2019 Vol. 34 No. 1 P. 1–13
A numerical algorithm is proposed for modeling two-component viscous compressible isothermal flows with surface effects in 3D domains of complex shape with a voxel representation of geometry. The regularized system of Navier-Stokes-Kahn-Hillard equations is used as a basic mathematical model. Modeling of the drop spreading on a flat substrate and the displacement of one liquid by ...
Added: September 28, 2018
Zlotnik A., Lomonosov T., Журнал вычислительной математики и математической физики 2019 Т. 59 № 3 С. 481–493
Изучаются явные двухслойные по времени и симметричные по пространству разностные схемы, построенные посредством аппроксимации 1D баротропных квазигазо/квазигидродинамических систем уравнений. Они линеаризуются на постоянном решении с ненулевой скоростью, и для них выводятся как необходимые, так и достаточные условия $L^2$-диссипативности решений задачи Коши в зависимости от числа Маха. Эти условия различаются между собой не более чем в 2 раза. Результаты ...
Added: September 26, 2018