The Research on the Axis-Symmetric Development and Verification for the Positive Scheme Numerical Method

2014 ◽  
Vol 1061-1062 ◽  
pp. 1096-1099
Author(s):  
Jian Lin Zhong ◽  
Gui Gao Le
Keyword(s):  
Numerical Simulation ◽  
Numerical Calculation ◽  
Numerical Method ◽  
Euler Equations ◽  
High Accuracy ◽  
The Self ◽  
Regular Reflection ◽  
Symmetric Flow ◽  
Positive Scheme ◽  
Oblique Shocks

The mathematic express of positive scheme axis-symmetric Euler equations is derived. With the numerical calculation of oblique shocks regular reflection problem, the validity of the positive scheme method and the self-programmed codes is verified. The positive scheme method is developed to solve the axis-symmetric Euler equations and then used to simulate the supersonic axis-symmetric flow over missile afterbody. The results show that: the numerical simulation match well with the experimental results and the numerical results obtained by the already existing high accuracy scheme method, the correctness of the development of positive scheme method is verified.

scholarly journals THE SELF-MODULATION OF STRONGLY NONLINEAR WATER WAVES. INCOMPLETE RECURRENCE

2019 ◽  
Vol 47 (1) ◽  
pp. 116-117
Author(s):  
A.V. Slunyaev ◽  
A.S. Dosaev
Keyword(s):  
Nonlinear Dynamics ◽  
Numerical Simulation ◽  
Euler Equations ◽  
Gravity Waves ◽  
Water Waves ◽  
Water Surface ◽  
The Self ◽  
Hydrodynamic Equations ◽  
Nonlinear Water Waves ◽  
Strongly Nonlinear

The processes of spontaneous self-modulation of steep gravity waves on the water surface with the formation of very short groups are investigated by means of the numerical simulation of the primitive Euler equations. It is shown that the subsequent demodulation is incomplete as a result of the generation of new waves with other lengths propagating both along the way and towards the main wave. Thus, in the framework of the full hydrodynamic equations an approximate analogue corresponds to the breather solution of the nonlinear Schrödinger equation. The parts of the research was supported by the RSF grant No 16-17-00041 and by the RAS Presidium Program «Nonlinear dynamics: fundamental problems and applications».

Numerical Method Research of Partial Differential Equations Inverse Problem

2011 ◽  
Vol 50-51 ◽  
pp. 455-458
Author(s):  
Ya Li He ◽  
Ya Mian Peng ◽  
Li Chao Feng
Keyword(s):  
Numerical Simulation ◽  
Genetic Algorithm ◽  
Inverse Problem ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Numerical Method ◽  
High Accuracy ◽  
Practical Application ◽  
Partial Differential ◽  
Comprehensive Coverage

It is feasible for the inverse problem of research in the very vital significance between in practical application. Genetic algorithm is applied in many aspects, but we are more concerned with the application in mathematics. From the start of genetic algorithm, the collection to search for comprehensive coverage of preferred. Due to genetic algorithm is used to search the information, and does not need such problems with the problem is directly related to the derivative of the information. Finally, the results of numerical simulation show that the GA method has high accuracy and quick convergent speed. And it is easy to program and calculate. It is worth of practical application.

scholarly journals Accuracy Problems of Numerical Calculation of Fractional Order Derivatives and Integrals Applying the Riemann-Liouville/Caputo Formulas

2016 ◽  
Vol 1 (1) ◽  
pp. 23-44 ◽  
Author(s):  
Dariusz W. Brzeziński
Keyword(s):  
Numerical Calculation ◽  
Numerical Method ◽  
Numerical Integration ◽  
Fractional Order ◽  
High Accuracy ◽  
Accuracy Improvement ◽  
Applied Method ◽  
Wide Range ◽  
Accuracy Increase ◽  
Actual Accuracy

AbstractIn the paper there are presented and evaluated for effectiveness three methods of accuracy increase of fractional order derivatives and integrals computations for application with the Riemann-Liouville/Caputo formulas. They are based on the ideas of either transforming difficult integrand in the formulas to high-accuracy computations requirements of a applied method of numerical integration or adapting a numerical method of integration to handle with high-accuracy a difficult feature in the integrand. Additional accuracy gain is obtained by incorporating increased precision into computations. The actual accuracy improvement by applying presented methods is compared with the capabilities of wide range of available methods of integration.

The Investigation of the Influence of Structure Parameters on the Friction-Induced Self-Excited Vibration

2011 ◽  
Vol 66-68 ◽  
pp. 933-936
Author(s):  
Xian Jie Meng
Keyword(s):  
Nonlinear Dynamics ◽  
Numerical Method ◽  
Calculation Result ◽  
Dry Friction ◽  
Vibration Amplitude ◽  
The Self ◽  
Structure Parameters ◽  
Dynamics Model ◽  
Excited Vibration ◽  
Nonlinear Dynamics Model

A one degree of freedom nonlinear dynamics model of self-excited vibration induced by dry-friction was built firstly, the numerical method was taken to study the impacts of structure parameters on self-excited vibration. The calculation result shows that the variation of stiffness can change the vibration amplitude and frequency of the self-excited vibration, but can not eliminate it, Along with the increase of system damping the self-excite vibration has the weakened trend and there a ritical damping, when damping is greater than it the self-excite vibration will be disappeared.

An Efficient Galerkin BEM to Compute High Acoustic Eigenfrequencies

2009 ◽  
Vol 131 (3) ◽  
Author(s):  
Mario Durán ◽  
Jean-Claude Nédélec ◽  
Sebastián Ossandón
Keyword(s):  
Numerical Method ◽  
Integral Equations ◽  
High Frequency ◽  
High Accuracy ◽  
Integral Representations ◽  
Stability And Convergence ◽  
Symmetric Matrices ◽  
Frequency Interval ◽  
Numerical Treatment ◽  
The Stability

An efficient numerical method, using integral equations, is developed to calculate precisely the acoustic eigenfrequencies and their associated eigenvectors, located in a given high frequency interval. It is currently known that the real symmetric matrices are well adapted to numerical treatment. However, we show that this is not the case when using integral representations to determine with high accuracy the spectrum of elliptic, and other related operators. Functions are evaluated only in the boundary of the domain, so very fine discretizations may be chosen to obtain high eigenfrequencies. We discuss the stability and convergence of the proposed method. Finally we show some examples.

Numerical Simulation of Shock Wave in Air Based on FCT Method

2013 ◽  
Vol 397-400 ◽  
pp. 270-273
Author(s):  
Ying Li ◽  
Xiao Bin Li ◽  
Yu Wang ◽  
Wei Zhang
Keyword(s):  
Numerical Simulation ◽  
Shock Wave ◽  
Comparative Analysis ◽  
Numerical Method ◽  
Blast Wave ◽  
Empirical Formula ◽  
Godunov Method ◽  
Numerical Accuracy

Blast wave is numerical simulated based on FCT method. According to the comparative analysis, taking Henrych empirical formula as a standard, FCT method is more accuracy than Godunov method. Moreover, it has been found that the numerical accuracy is insufficient when the distance is small, it is necessary to develop and modify the numerical method continuously.

Numerical Simulation of Driven Piles in Alluvial Soil

2011 ◽  
Vol 105-107 ◽  
pp. 1415-1419 ◽  
Author(s):  
Shih Tsung Hsu
Keyword(s):  
Numerical Simulation ◽  
Numerical Method ◽  
Alluvial Soil ◽  
Field Tests ◽  
Driven Piles ◽  
Driven Pile

This study developed a numerical method to establish a comprehensive load-settlement curve for a driven pile. Analysis results shown that the residual forces caused by the driving of the pile can be simulated using the numerical method that proposed herein. The load was applied to the tested piles, while the incremental displacement was subjected to numerical piles. Although these two processes are distinctive, the load-settlement behaviors of various piles calculated numerically are consistent with those measured from field tests. Moreover, the proposed numerical method highlighted the post-peak behavior of a pile. Accordingly, the numerical method was very suitable to analyze the behavior of driven piles.

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