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基于层次模型的雷诺方程自适应变步长差分算法研究
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武汉科技大学冶金装备及其控制教育部重点实验室开放基金项目(2015B14).


Research on Adaptive Stepsize Difference Algorithm for Reynolds Equation Based on Hierarchical Model
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    摘要:

    针对传统有限差分法求解雷诺方程效率低和灵活性差等问题,提出一种基于网格层次化思想的差分算法来求解雷诺方程模型。首先建立变步长雷诺方程差分计算模型,然后提出基于压力梯度与区域积分值的区域细化算法,最后基于层次化思想给出自适应变步长差分算法的求解流程。该方法采用网格层次化思想将初始粗网格进行不断的校正,模拟构造出能满足目标的自适应网格,有效地避免了传统等分网格方法为提高求解精度而不断盲目细化风格的问题。通过不同模型的计算结果表明:基于层次化思想的自适应变步长差分算法相较传统的等分网格有限差分算法,能够用较小的自由度计算得到较好的表达油膜压力的曲面,在求解效率和灵活性上有显著提升。

    Abstract:

    In order to solve the problem of low efficiency and poor flexibility in solving Reynolds equation by the traditional finite difference method,a difference algorithm based on the hierarchical idea was proposed to solve the Reynolds equation model.The variable step Reynolds equation difference calculation model was set up first,and then the thinning region algorithm based on the pressure gradient change and the region integral value was developed.Finally,the solution process and method of the adaptive variable step difference algorithm were realized.This method uses the hierarchical idea to continuously correct the initial coarse mesh,and simulate and construct adaptive grid that satisfies the target,which effectively avoids the problem of blind refinement mesh of the traditional equivalent mesh method in order to improve the accuracy of the solution.The results of different models show that the adaptive variable step length difference algorithm based on the hierarchical idea can obtain better surface of oil film pressure with smaller degree of freedom compared with the traditional finite difference algorithm.It has a significant improvement in efficiency and flexibility.

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张希,罗会信,左兵权,李子强.基于层次模型的雷诺方程自适应变步长差分算法研究[J].润滑与密封,2019,44(7):123-130.
. Research on Adaptive Stepsize Difference Algorithm for Reynolds Equation Based on Hierarchical Model[J]. Lubrication Engineering,2019,44(7):123-130.

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  • 在线发布日期: 2020-03-12
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