JUSTIFICATION OF THE AVERAGING METHOD FOR A SYSTEM OF EQUATIONS WITH THE NAVIER-STOKES OPERATOR IN THE PRINCIPAL PART

Levenshtam V. B.

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JUSTIFICATION OF THE AVERAGING METHOD FOR A SYSTEM OF EQUATIONS WITH THE NAVIER-STOKES OPERATOR IN THE PRINCIPAL PART

机译：主要部分用纳维斯托克斯算子对方程组求平均的方法的证明

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The averaging method is justified for a system of partial differential equations with the Navier-Stokes operator in the principal part. The right-hand side of this system (an analog of a mass force) oscillates in time with frequency omega 1, depends polynomially on the unknown (an analog of the flow velocity), and involves a linear summand proportional to root omega An initial-boundary value problem and a problem on time-periodic solutions are considered.

机译：对于以Navier-Stokes算子为主体的偏微分方程组，证明了平均方法的合理性。该系统的右手侧（质量力的模拟物）以omega 1的频率及时振荡。多项式取决于未知数（流速的模拟物），并且涉及与根欧米茄成正比的线性求和。考虑了初边值问题和时间周期解的问题。

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《St. Petersburg mathematical journal》 |2015年第1期|共22页
作者
Levenshtam V. B.;
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正文语种 eng
中图分类数学;
关键词
Partial differential equations; Navier-Stokes operator; rapidly oscillating summands; averaging method;

机译：偏微分方程;Navier-Stokes算子;快速振荡求和;求平均;

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专利

1. JUSTIFICATION OF THE AVERAGING METHOD FOR A SYSTEM OF EQUATIONS WITH THE NAVIER-STOKES OPERATOR IN THE PRINCIPAL PART [J] . Levenshtam V. B. St. Petersburg mathematical journal . 2015,第1期

机译：主要部分用纳维斯托克斯算子对方程组求平均的方法的证明
2. To the justification of the general projection method for solving linear integral equations with a fractional Riemann-Liouville integral in the principal part [J] . J R Agachev, A F Galimyanov Journal of Physics: Conference Series . 2019,第2期

机译：为了证明一般投影方法求解主要部分为分数Riemann-Liouville积分的线性积分方程
3. Justification of the Averaging Method for Differential Equations with Large Rapidly Oscillating Summands and Boundary Conditions [J] . V. B. Levenshtam, P. E. Shubin Mathematical notes . 2016,第1a2期

机译：具有大的快速振荡和边界条件的微分方程平均法的证明
4. Computer Aided Analysis of Preconditioned Multistage Runge-Kutta Methods Applied to Solve the Compressible Reynolds Averaged Navier-Stokes Equations [C] . Stefan Langer STAB/DGLR Symposium . 2016

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5. Application of High-Order Summation-by-Parts Operators to the Steady Reynolds-Averaged Navier-Stokes Equations [D] . Shen, Xiaoyue. 2017

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6. Assessment of air flow distribution and hazardous release dispersion around a single obstacle using Reynolds-averaged Navier-Stokes equations [O] . Konstantinos Vasilopoulos, Ioannis E. Sarris, Panagiotis Tsoutsanis 2019

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7. Analysis of Influence of the Thermal Dependence of Air Thermophysical Properties on the Accuracy of Simulation of Heat Transfer in a Turbulent Flow in Case of Applying Different Methods of Averaging Navier-Stokes Equations [O] . A. D. Kliukvin 2014

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8. Numerical Methods for Coupling the Reynolds-Averaged Navier-Stokes Equations withthe Reynolds-Stress Turbulence Model [R] . Rautaheimo, P., Siikonen, T. 1995

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JUSTIFICATION OF THE AVERAGING METHOD FOR A SYSTEM OF EQUATIONS WITH THE NAVIER-STOKES OPERATOR IN THE PRINCIPAL PART

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