scholarly journals Dynamic Stability of Plane Free Surface of Liquid in Axisymmetric Tanks

2013 ◽  
Vol 2013 ◽  
pp. 1-16 ◽  
Author(s):  
Siva Srinivas Kolukula ◽  
P. Chellapandi
Keyword(s):  
Free Surface ◽  
Parametric Instability ◽  
Nonlinear Finite Element ◽  
Linear Potential ◽  
Kutta Method ◽  
Nonlinear Finite Element Method ◽  
Time Step ◽  
Runge Kutta Method ◽  
Numerical Instabilities ◽  
The Stability

When liquid filled containers are excited vertically, it is known that, for some combinations of frequency and amplitude, the free surface undergoes unbounded motion leading to instability, called parametric instability or parametric resonance, while for other combinations the free surface remains plane. In this paper, the stability of the plane free surface is investigated theoretically when the vessel is a vertical axisymmetric container. The effect of coupled horizontal excitation on the stability is examined. The dynamics of sloshing flows under specified excitations are simulated numerically using fully nonlinear finite element method based on non-linear potential flow theory. A mixed Eulerian-Lagrangian technique combined with 4th-order Runge-Kutta method is employed to advance the solution in time. A regridding technique based on cubic spline is applied to the free surface for every finite time step to avoid possible numerical instabilities.

Application of the piecewise constant method in nonlinear dynamics of drill string

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Jialin Tian ◽  
Jie Wang ◽  
Yi Zhou ◽  
Lin Yang ◽  
Changyue Fan ◽  
...  
Keyword(s):  
Nonlinear Dynamics ◽  
Dynamic Model ◽  
Dynamic Characteristics ◽  
Drill String ◽  
Vibration Velocity ◽  
Kutta Method ◽  
Time Step ◽  
Piecewise Constant ◽  
Runge Kutta Method ◽  
Runge Kutta

Abstract Aiming at the current development of drilling technology and the deepening of oil and gas exploration, we focus on better studying the nonlinear dynamic characteristics of the drill string under complex working conditions and knowing the real movement of the drill string during drilling. This paper firstly combines the actual situation of the well to establish the dynamic model of the horizontal drill string, and analyzes the dynamic characteristics, giving the expression of the force of each part of the model. Secondly, it introduces the piecewise constant method (simply known as PT method), and gives the solution equation. Then according to the basic parameters, the axial vibration displacement and vibration velocity at the test points are solved by the PT method and the Runge–Kutta method, respectively, and the phase diagram, the Poincare map, and the spectrogram are obtained. The results obtained by the two methods are compared and analyzed. Finally, the relevant experimental tests are carried out. It shows that the results of the dynamic model of the horizontal drill string are basically consistent with the results obtained by the actual test, which verifies the validity of the dynamic model and the correctness of the calculated results. When solving the drill string nonlinear dynamics, the results of the PT method is closer to the theoretical solution than that of the Runge–Kutta method with the same order and time step. And the PT method is better than the Runge–Kutta method with the same order in smoothness and continuity in solving the drill string nonlinear dynamics.

Transport Schemes in GungHo

2021 ◽  
Author(s):  
James Kent
Keyword(s):  
Finite Element ◽  
Finite Volume ◽  
Mixed Finite Element ◽  
Method Of Lines ◽  
Finite Volume Methods ◽  
Kutta Method ◽  
Finite Volume Schemes ◽  
Dynamical Core ◽  
Runge Kutta Method ◽  
The Stability

<p>GungHo is the mixed finite-element dynamical core under development by the Met Office. A key component of the dynamical core is the transport scheme, which advects density, temperature, moisture, and the winds, throughout the atmosphere. Transport in GungHo is performed by finite-volume methods, to ensure conservation of certain quantaties. There are a range of different finite-volume schemes being considered for transport, including the Runge-Kutta/method-of-lines and COSMIC/Lin-Rood schemes. Additional horizontal/vertical splitting approaches are also under consideration, to improve the stability aspects of the model. Here we discuss these transport options and present results from the GungHo framework, featuring both prescribed velocity advection tests and full dry dynamical core tests. </p>

scholarly journals Numerical Study on Phase-Fitted and Amplification-Fitted Diagonally Implicit Two Derivative Runge-Kutta Method for Periodic IVPS

2021 ◽  
Vol 50 (6) ◽  
pp. 1799-1814
Author(s):  
Norazak Senu ◽  
Nur Amirah Ahmad ◽  
Zarina Bibi Ibrahim ◽  
Mohamed Othman
Keyword(s):  
Fourth Order ◽  
Initial Value Problems ◽  
Numerical Experiments ◽  
Numerical Study ◽  
Kutta Method ◽  
Initial Value ◽  
First Order ◽  
Runge Kutta Method ◽  
Runge Kutta ◽  
The Stability

A fourth-order two stage Phase-fitted and Amplification-fitted Diagonally Implicit Two Derivative Runge-Kutta method (PFAFDITDRK) for the numerical integration of first-order Initial Value Problems (IVPs) which exhibits periodic solutions are constructed. The Phase-Fitted and Amplification-Fitted property are discussed thoroughly in this paper. The stability of the method proposed are also given herewith. Runge-Kutta (RK) methods of the similar property are chosen in the literature for the purpose of comparison by carrying out numerical experiments to justify the accuracy and the effectiveness of the derived method.

Slope Safety of Earth Rockfill Cofferdam with Nonlinear Shear Strength

2011 ◽  
Vol 243-249 ◽  
pp. 4472-4477
Author(s):  
Xiao Chun Lu ◽  
Bin Tian ◽  
Yan Fu Qin
Keyword(s):  
Shear Strength ◽  
Nonlinear Finite Element ◽  
Nonlinear Finite Element Method ◽  
Analysis Method ◽  
Seepage Field ◽  
Construction Period ◽  
Practical Project ◽  
The Stability ◽  
Nonlinear Shear ◽  
Effective Analysis

Based on numerical simulation of the seepage field of earth rockfill cofferdam using nonlinear Finite Element Method under the action of flood during construction period, the stability of the cofferdam slope with nonlinear shear strength is studied. The effectiveness and applicability of the method introduced in the paper is certified through computation in the study on the practical project. The paper provides an effective analysis method for the study on the stability of dam slope of earth rockfill cofferdam.

Numerical Simulation of the Water Entry of Two-Dimensional Body with Flow Separation

2011 ◽  
Vol 138-139 ◽  
pp. 376-381 ◽  
Author(s):  
Yun Bo Li ◽  
Ya Jun Li ◽  
Yan Wang
Keyword(s):  
Free Surface ◽  
Flow Separation ◽  
Water Entry ◽  
Two Dimensional ◽  
Numerical Result ◽  
Runge Kutta Method ◽  
Theory Result ◽  
The Stability ◽  
Stability And Accuracy ◽  
Good Agreement

The water entry of two-dimensional body with flow separation is simulated based on potential theory and boundary element method. The double point model and four-order Runge-Kutta method and jet-cut model and free surface smooth technique and regrinding technique are used to assure the stability and accuracy of the numerical result. A flow separation model is introduced to simulate the water entry of two-dimensional body with knuckle. The free surface elevation and pressure distribution of wedge with knuckle are predicted and compared with other theory result. Good agreement between numerical result and other theory result is indicated that the numerical method is stability and effective.

scholarly journals Numerical calculation for coupling vibration system by Piecewise-Laplace method

2020 ◽  
Vol 103 (3) ◽  
pp. 003685042093855
Author(s):  
Pan Fang ◽  
Kexin Wang ◽  
Liming Dai ◽  
Chixiang Zhang
Keyword(s):  
Numerical Computation ◽  
Laplace Transformation ◽  
Original System ◽  
Continuity Condition ◽  
Kutta Method ◽  
Laplace Method ◽  
Time Step ◽  
Coupling Vibration ◽  
Runge Kutta Method ◽  
Runge Kutta

To improve the reliability and accuracy of dynamic machine in design process, high precision and efficiency of numerical computation is essential means to identify dynamic characteristics of mechanical system. In this paper, a new computation approach is introduced to improve accuracy and efficiency of computation for coupling vibrating system. The proposed method is a combination of piecewise constant method and Laplace transformation, which is simply called as Piecewise-Laplace method. In the solving process of the proposed method, the dynamic system is first sliced by a series of continuous segments to reserve physical attribute of the original system; Laplace transformation is employed to separate coupling variables in segment system, and solutions of system in complex domain can be determined; then, considering reverse Laplace transformation and residues theorem, solution in time domain can be obtained; finally, semi-analytical solution of system is given based on continuity condition. Through comparison of numerical computation, it can be found that precision and efficiency of numerical results with the Piecewise-Laplace method is better than Runge-Kutta method within same time step. If a high-accuracy solution is required, the Piecewise-Laplace method is more suitable than Runge-Kutta method.

Character of Embankment Reinforced with Geotextile on Sloping Weak Foundation

2010 ◽  
Vol 168-170 ◽  
pp. 1272-1276
Author(s):  
Jin Long Liu ◽  
Jie Qun Liu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Plastic Zone ◽  
Lateral Displacement ◽  
Nonlinear Finite Element ◽  
Nonlinear Finite Element Method ◽  
The Stability ◽  
Peak Value ◽  
Element Method

Based on nonlinear finite element method, the character of embankment reinforced with geotextile on sloping weak foundation has been studied. It is shown that the lateral displacement of embankment has been distinctly effected by the sloping of foundation, the value of lateral displacement on sloping foundation is greatly bigger than that of horizontal foundation. The peak value of lateral displacement can be effectively reduced by geotextile. With the same condition, geotextile in sloping foundation acts a more important effect than that of horizontal foundation. The development of plastic zone of embankment has been impeded and separated by geotextile, which enhanced the stability of embankment. The results also indicated that, if necessary, reinforcement such as anti-slide pile should be layout at lower toe of embankment on sloping weak foundation.

Study on Stability Round Stronger Axis of the Column with Composite Section of Double Limbs under Axial Compression

2010 ◽  
Vol 163-167 ◽  
pp. 633-640
Author(s):  
Deng Feng Wang ◽  
Yuan Qing Wang ◽  
Yong Jiu Shi ◽  
Bin Fang
Keyword(s):  
Axial Compression ◽  
Electrostatic Precipitator ◽  
Nonlinear Finite Element ◽  
Thickness Ratio ◽  
Nonlinear Finite Element Method ◽  
Stability Performance ◽  
Composite Section ◽  
Geometrical Imperfections ◽  
The Stability ◽  
Flexural Torsional Buckling

The section of the column under axial compression used in a certain electrostatic precipitator is composed of double H shaped steel limbs and the stiffened connecting web by weld. As the width of connecting web usually exceeds 3 times of the section height of H shaped steel, the axis which connecting web lies in is the weaker axis for the stiffness of column section, while the midperpendicular of connecting web is the stronger axis. In consideration of initial geometrical imperfections and weld residual stresses, the study on stability round the stronger axis of column subjected to axial compression by nonlinear finite element method is conducted. The research results indicate that the column doesn’t present the flexural buckling round the stronger axis, but present the elasto-plastic flexural-torsional buckling. A buckling factor is produced to measure the stability performance of column round stronger axis. When the connecting channel shaped steels between two limbs and the stiffeners located on connecting web are strengthened, the buckling factor increases slightly. When the width-thickness ratio of connecting web increases, the buckling factor decreases significantly. When the slenderness of H shaped steel round the stronger axis is kept constant and the height-thickness ratio of H-shaped steel web increases, the buckling factor increases. Based on a great many computation results, the regressed recommendation is proposed how to evaluate the design buckling bearing capacity of column under axial compression round stronger axis.

A FOURTH ORDER DIFFERENCE SCHEME FOR THE MAXWELL EQUATIONS ON YEE GRID

2008 ◽  
Vol 05 (03) ◽  
pp. 613-642 ◽  
Author(s):  
ALY FATHY ◽  
CHENG WANG ◽  
JOSHUA WILSON ◽  
SONGNAN YANG
Keyword(s):  
Fourth Order ◽  
Maxwell Equations ◽  
Numerical Solutions ◽  
Stability Domain ◽  
Time Step ◽  
Runge Kutta Method ◽  
Accuracy Check ◽  
Grid Points ◽  
The Stability ◽  
Magnetic Vectors

The Maxwell equations are solved by a long-stencil fourth order finite difference method over a Yee grid, in which different physical variables are located at staggered mesh points. A careful treatment of the numerical values near the boundary is introduced, which in turn leads to a "symmetric image" formula at the "ghost" grid points. Such a symmetric formula assures the stability of the boundary extrapolation. In turn, the fourth order discrete curl operator for the electric and magnetic vectors gives a complete set of eigenvalues in the purely imaginary axis. To advance the dynamic equations, the four-stage Runge–Kutta method is utilized, which results in a full fourth order accuracy in both time and space. A stability constraint for the time step is formulated at both the theoretical and numerical levels, using an argument of stability domain. An accuracy check is presented to verify the fourth order precision, using a comparison between exact solution and numerical solutions at a fixed final time. In addition, some numerical simulations of a loss-less rectangular cavity are also carried out and the frequency is measured precisely.

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