A stability preserved time-integration method for nonlinear advection–diffusion-reaction processes

Based on the newly proposed generalized Galerkin weak form (GGW) method, a two-step time integration method with controllable numerical dissipation is presented. In the first sub-step, the GGW method is used, and in the second sub-step, a new parameter is introduced by using the idea of a trapezoidal integral. According to the numerical analysis, it can be concluded that this method is unconditionally stable and its numerical damping is controllable with the change in introduced parameters. Compared with the GGW method, this two-step scheme avoids the fast numerical dissipation in a low-frequency range. To highlight the performance of the proposed method, some numerical problems are presented and illustrated which show that this method possesses superior accuracy, stability and efficiency compared with conventional trapezoidal rule, the Wilson method, and the Bathe method. High accuracy in a low-frequency range and controllable numerical dissipation in a high-frequency range are both the merits of the method.

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An energy‐conserving and decaying time integration method for general nonlinear dynamics

International Journal for Numerical Methods in Engineering ◽

10.1002/nme.6251 ◽

2019 ◽

Vol 121 (5) ◽

pp. 925-944 ◽

Cited By ~ 1

Author(s):

H. M. Zhang ◽

Y. F. Xing ◽

Y. Ji

Keyword(s):

Nonlinear Dynamics ◽

Integration Method ◽

Time Integration ◽

Time Integration Method ◽

Energy Conserving

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

Journal of Physics Conference Series ◽

10.1088/1742-6596/2090/1/012145 ◽

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.

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