宋佳, 许成顺, 杜修力, 李亮. 基于精细时程积分的u-p格式饱和两相介质动力问题的显-显式时域算法[J]. 工程力学, 2017, 34(11): 9-17. DOI: 10.6052/j.issn.1000-4750.2016.04.0257
引用本文: 宋佳, 许成顺, 杜修力, 李亮. 基于精细时程积分的u-p格式饱和两相介质动力问题的显-显式时域算法[J]. 工程力学, 2017, 34(11): 9-17. DOI: 10.6052/j.issn.1000-4750.2016.04.0257
SONG Jia, XU Cheng-shun, DU Xiu-li, LI Liang. A TEMPORAL EXPLICIT-EXPLICIT ALGORITHM BASED ON THE PRECISE TIME-INTEGRATION FOR SOLVING THE DYNAMIC PROBLEMS OF FLUID-SATURATED POROUS MEDIA IN u-p FORM[J]. Engineering Mechanics, 2017, 34(11): 9-17. DOI: 10.6052/j.issn.1000-4750.2016.04.0257
Citation: SONG Jia, XU Cheng-shun, DU Xiu-li, LI Liang. A TEMPORAL EXPLICIT-EXPLICIT ALGORITHM BASED ON THE PRECISE TIME-INTEGRATION FOR SOLVING THE DYNAMIC PROBLEMS OF FLUID-SATURATED POROUS MEDIA IN u-p FORM[J]. Engineering Mechanics, 2017, 34(11): 9-17. DOI: 10.6052/j.issn.1000-4750.2016.04.0257

基于精细时程积分的u-p格式饱和两相介质动力问题的显-显式时域算法

A TEMPORAL EXPLICIT-EXPLICIT ALGORITHM BASED ON THE PRECISE TIME-INTEGRATION FOR SOLVING THE DYNAMIC PROBLEMS OF FLUID-SATURATED POROUS MEDIA IN u-p FORM

  • 摘要: 时域算法的计算效率是求解实际非线性或大量自由度等工程问题最重要的影响因素,而显式算法是提高计算效率最有效的手段。针对 u -p格式饱和两相介质动力方程,实现显-显式算法的必要前提是质量矩阵 M 和流体压缩矩阵 S 的对角化处理,且整体算法的计算精度和稳定性同样需要权衡。基于对角化的 MS 矩阵,将高精度和稳定性的精细时程积分法应用于求解液相方程,并结合求解固、液两相动力方程的中心差分法,提出了一种新的显-显式的高效时域算法。理论分析和数值试验结果均说明提出方法具有良好的稳定性和较高的计算精度。

     

    Abstract: The computational efficiency of temporal algorithms has a great influence on solving actual engineering problems with nonlinearity or numerous degrees of freedom. The explicit algorithm is one of the most effective methods to improve the efficiency. For the fluid-saturated porous media in the u -p form, the realization of the explicit-explicit algorithm depends on the diagonal mass matrix M and fluid compressibility matrix S . The accuracy and stabilization of complete algorithm also need to be considered as well. In this paper, based on the diagonalization of M and S matrices, the precise time-integration with characters of high-accuracy and stabilization was introduced to solve the fluid phase equation, and the central difference method was used to solve the solid-fluid complete dynamic equation. Consisting of the two methods, a novel efficiently explicit-explicit algorithm was proposed. A high level of stability and accuracy of the algorithm was verified by theoretical analysis and numerical examples.

     

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