On a Large Time-Stepping Method for the Swift-Hohenberg Equation

AbstractThe main purpose of this work is to contrast and analyze a large time-stepping numerical method for the Swift-Hohenberg (SH) equation. This model requires very large time simulation to reach steady state, so developing a large time step algorithm becomes necessary to improve the computational efficiency. In this paper, a semi-implicit Euler schemes in time is adopted. An extra artificial term is added to the discretized system in order to preserve the energy stability unconditionally. The stability property is proved rigorously based on an energy approach. Numerical experiments are used to demonstrate the effectiveness of the large time-stepping approaches by comparing with the classical scheme.

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Numerical Simulation of Transient Flow in Products Pipeline

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.732-733.487 ◽

2013 ◽

Vol 732-733 ◽

pp. 487-490

Author(s):

Zhen Ye Wang ◽

Jiang Fei Li ◽

Lian Yuan ◽

Zhi Zhong Fu ◽

Bo Li ◽

...

Keyword(s):

Difference Scheme ◽

Large Time ◽

Transient Flow ◽

Implicit Difference Scheme ◽

Time Step ◽

Characteristics Method ◽

Large Time Step ◽

The Stability ◽

Products Pipeline ◽

Stability And Accuracy

In this paper, explicit difference scheme, implicit difference scheme and characteristics method are separately used to simulate the transient flow in products pipeline. The simulation result can be used to prevent water hammer in the pipeline of unsteady situation and to improve the efficiency and safety in oil transmission systems. And then, the stability and accuracy of the three methods are compared by adopting different time steps. For explicit difference method, large fluctuation may occur in case of large time step. For implicit method, the result is weakly affected by time step, only if the relaxation factor selected is reasonable. For characteristics method, the results have a high convergence speed and precision. The results show that, in the situation of valve shut down in terminal, it takes about 1.1×104 seconds to return to a new steady state.

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An integrated explicit–implicit algorithm for vehicle–rail–bridge dynamic simulations

Proceedings of the Institution of Mechanical Engineers Part F Journal of Rail and Rapid Transit ◽

10.1177/0954409717753210 ◽

2018 ◽

Vol 232 (6) ◽

pp. 1895-1913 ◽

Cited By ~ 4

Author(s):

Zhibin Jin ◽

Chuanchuan Hu ◽

Shiling Pei ◽

Hongyan Liu

Keyword(s):

Large Scale ◽

Large Time ◽

Dynamic Interaction ◽

Degree Of Freedom ◽

Time Step ◽

Single Time ◽

Large Time Step ◽

Step Algorithm ◽

Bridge Responses ◽

Two Degree Of Freedom

The dynamic interaction between the vehicle, rail, and bridges presents a huge computational challenge, especially for reliability analysis based on Monte Carlo simulations. In this study, an integrated algorithm is proposed for the vehicle–rail–bridge dynamic interaction problem. This algorithm divides the system into two subdomains, i.e. the vehicle–rail subdomain and the bridge subdomain. The vehicle–rail subdomain and the bridge subdomain are integrated by the Zhai algorithm and the Newmark-β algorithm, respectively. The integrated algorithm allows different time steps (or multitime steps) to be used for the two domains: a large time step for the bridge subdomain and a smaller one for the vehicle–rail subdomain. The stability region of the proposed algorithm was found through the two-degree-of-freedom model problem, when a single time step is used in both subdomains. The accuracy of the algorithm was numerically investigated through the two-degree-of-freedom model. The vehicle–rail–bridge vibration excited by rail irregularities and earthquakes was simulated using the multitime step algorithm. The effect of the time step ratio (ratio of the large time step to the small time step) on the accuracy of the vehicle–rail–bridge responses was investigated. It has been shown that the time step ratio of less than 50 produces vehicle–rail–bridge responses in an accurate manner for engineering purposes. The multitime step algorithm can solve the vehicle–rail–bridge problem 20 times faster than the single time step algorithms that are conventionally used in the vehicle–rail–bridge simulations. This multitime step algorithm provides an efficient alternative for solving the dynamic interaction between vehicle–rail and large-scale civil structures.

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