A quadratic b-spline based isogeometric analysis of transient wave propagation problems with implicit time integration method

2018 ◽  
Vol 59 ◽  
pp. 115-131 ◽  
Author(s):  
Weibin Wen ◽  
Shengyu Duan ◽  
Kai Wei ◽  
Yongbin Ma ◽  
Daining Fang
Keyword(s):  
Wave Propagation ◽  
Isogeometric Analysis ◽  
Integration Method ◽  
Time Integration ◽  
Implicit Time ◽  
Transient Wave ◽  
B Spline ◽  
Time Integration Method ◽  
Implicit Time Integration ◽  
Transient Wave Propagation

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.

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