scholarly journals Modeling Three‐Dimensional Wave Propagation in Anelastic Models With Surface Topography by the Optimal Strong Stability Preserving Runge‐Kutta Method

2019 ◽  
Vol 124 (1) ◽  
pp. 890-907 ◽  
Author(s):  
Nian Wang ◽  
Jiahang Li ◽  
Dmitry Borisov ◽  
Hom Nath Gharti ◽  
Yang Shen ◽  
...  
Keyword(s):  
Wave Propagation ◽  
Surface Topography ◽  
Three Dimensional ◽  
Strong Stability ◽  
Kutta Method ◽  
Strong Stability Preserving ◽  
Runge Kutta Method ◽  
Runge Kutta ◽  
Dimensional Wave

Numerical Simulations of a Polydisperse Sedimentation Model by Using Spectral WENO Method with Adaptive Multiresolution

2016 ◽  
Vol 13 (06) ◽  
pp. 1650037
Author(s):  
Carlos A. Vega ◽  
Francisco Arias
Keyword(s):  
Convergence Rates ◽  
Time Discretization ◽  
Strong Stability ◽  
Kutta Method ◽  
Strong Stability Preserving ◽  
Third Order ◽  
Runge Kutta Method ◽  
Sedimentation Model ◽  
Runge Kutta ◽  
Fifth Order

In this work, we apply adaptive multiresolution (Harten’s approach) characteristic-wise fifth-order Weighted Essentially Non-Oscillatory (WENO) for computing the numerical solution of a polydisperse sedimentation model, namely, the Höfler and Schwarzer model. In comparison to other related works, time discretization is carried out with the ten-stage fourth-order strong stability preserving Runge–Kutta method which is more efficient than the widely used optimal third-order TVD Runge–Kutta method. Numerical results with errors, convergence rates and CPU times are included for four and 11 species.

Explicit Runge-Kutta method for three-dimensional internal incompressible flows

AIAA Journal ◽  
1992 ◽  
Vol 30 (8) ◽  
pp. 2024-2031 ◽  
Author(s):  
H. Cabuk ◽  
C.-H Sung ◽  
V. Modi
Keyword(s):  
Incompressible Flows ◽  
Three Dimensional ◽  
Kutta Method ◽  
Runge Kutta Method ◽  
Runge Kutta

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.

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