Abstract A new completely explicit algorithm is developed to solve the dynamic u-p formation of fluid-saturated porous media. The mass matrix and the fluid compressibility matrix are diagonalized in the spatial domain. The central difference method, Lagrange quadratic interpolation and Taylor-series method are employed to solve the u-p formed equations in the time domain. The analysis for the theoretical accuracy and stability of the proposed method indicates that the new algorithm has second-order accuracy and is conditionally stable. Four examples are given to demonstrate the effectiveness of the proposed algorithm by comparing the solutions with those obtained by the analytical method, the explicit-implicit method developed by Zienkiewicz et al. and the explicit-explicit method developed by Xu et al. The comparison results indicate that the present method is accurate, also allow larger time step than that of Xu et al.

中文翻译：

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求解饱和土动力-p方程的一种新的完全显式算法

摘要 开发了一种新的完全显式算法来求解流体饱和多孔介质的动态向上地层问题。质量矩阵和流体压缩性矩阵在空间域中对角化。采用中心差分法、拉格朗日二次插值法和泰勒级数法在时域上求解向上形成的方程。对所提方法的理论精度和稳定性的分析表明，新算法具有二阶精度，并且是条件稳定的。给出了四个例子，通过将解与解析方法获得的解进行比较来证明所提出算法的有效性，解析方法是由 Zienkiewicz 等人开发的显式隐式方法。以及由 Xu 等人开发的显式-显式方法。