Insight to the Newmark Implicit Time Integration Method for Solving the Wave Propagation Problems

2021 ◽  
Author(s):  
Sobhan Rostami ◽  
Reza Kamgar
Keyword(s):  
Wave Propagation ◽  
Integration Method ◽  
Time Integration ◽  
Implicit Time ◽  
Time Integration Method ◽  
Implicit Time Integration

scholarly journals Impact of difference between explicit and implicit second-order time integration schemes on isotropic/anisotropic steady incompressible turbulence field

2021 ◽  
Vol 2090 (1) ◽  
pp. 012145
Author(s):  
Ryuma Honda ◽  
Hiroki Suzuki ◽  
Shinsuke Mochizuki
Keyword(s):  
Kinetic Energy ◽  
Energy Conservation ◽  
Integration Method ◽  
Time Integration ◽  
Second Order ◽  
Implicit Time ◽  
Explicit Time Integration ◽  
Time Integration Method ◽  
Implicit Time Integration ◽  
Time Integration Methods

Abstract This study presents the impact of the difference between the implicit and explicit time integration methods on a steady turbulent flow field. In contrast to the explicit time integration method, the implicit time integration method may produce significant kinetic energy conservation error because the widely used spatial difference method for discretizing the governing equations is explicit with respect to time. In this study, the second-order Crank-Nicolson method is used as the implicit time integration method, and the fourth-order Runge-Kutta, second-order Runge-Kutta and second-order Adams-Bashforth methods are used as explicit time integration methods. In the present study, both isotropic and anisotropic steady turbulent fields are analyzed with two values of the Reynolds number. The turbulent kinetic energy in the steady turbulent field is hardly affected by the kinetic energy conservation error. The rms values of static pressure fluctuation are significantly sensitive to the kinetic energy conservation error. These results are examined by varying the time increment value. These results are also discussed by visualizing the large scale turbulent vortex structure.

MESHFREE COLLOCATION METHOD FOR IMPLICIT TIME INTEGRATION OF ODES

2011 ◽  
Vol 08 (01) ◽  
pp. 119-137 ◽  
Author(s):  
HENNADIY NETUZHYLOV ◽  
ANDREAS ZILIAN
Keyword(s):  
Collocation Method ◽  
Integration Method ◽  
Time Integration ◽  
Implicit Time ◽  
Lorenz Equations ◽  
Foucault Pendulum ◽  
Time Integration Method ◽  
Implicit Time Integration ◽  
Typical Trajectory ◽  
Singular Weights

An implicit time integration meshfree collocation method for solving linear and nonlinear ordinary differential equations (ODEs) based on interpolating moving least squares technique, which uses singular weights for constructing ansatz functions, is presented. On an example of a system of equations for Foucault pendulum, the flexibility of the proposed approach is shown and the accuracy, convergence, and stability properties are investigated. In a nonlinear case, the method gives accurate results, which is demonstrated by the solution of Lorenz equations. The typical trajectory patterns, e.g. butterfly pattern, were observed and the properties of the method are compared to those of a higher-order time integration method.

scholarly journals A novel explicit three-sub-step time integration method for wave propagation problems

2022 ◽  
Author(s):  
Huimin Zhang ◽  
Runsen Zhang ◽  
Andrea Zanoni ◽  
Yufeng Xing ◽  
Pierangelo Masarati
Keyword(s):  
Wave Propagation ◽  
Integration Method ◽  
Time Integration ◽  
Second Order ◽  
New Method ◽  
Explicit Methods ◽  
Time Integration Method ◽  
Numerical Performance ◽  
The Stability ◽  
Better Than

AbstractA novel explicit three-sub-step time integration method is proposed. From linear analysis, it is designed to have at least second-order accuracy, tunable stability interval, tunable algorithmic dissipation and no overshooting behaviour. A distinctive feature is that the size of its stability interval can be adjusted to control the properties of the method. With the largest stability interval, the new method has better amplitude accuracy and smaller dispersion error for wave propagation problems, compared with some existing second-order explicit methods, and as the stability interval narrows, it shows improved period accuracy and stronger algorithmic dissipation. By selecting an appropriate stability interval, the proposed method can achieve properties better than or close to existing second-order methods, and by increasing or reducing the stability interval, it can be used with higher efficiency or stronger dissipation. The new method is applied to solve some illustrative wave propagation examples, and its numerical performance is compared with those of several widely used explicit methods.

Sign in / Sign up

Export Citation Format

Share Document