Stabilized low‐order finite elements for strongly coupled poromechanical problems
Stabilized low‐order finite elements for strongly coupled poromechanical problems
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DOI：
10.1002/nme.5815
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发表时间：
2018-08
影响因子：
2.9
通讯作者：
Wentao Li;Changfu Wei
中科院分区：
文献类型：
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作者：
Wentao Li;Changfu Wei
孔隙力学问题的有限元解通常在低渗透率、快速加载速率、粗网格和/或小时间步长的极限下表现出振荡的孔隙压力。为了完全抑制孔隙压力振荡，提出了一种具有较好单调性的稳定有限元格式来模拟可压缩流体-饱和多孔介质。该方法基于多项式压力投影技术，允许对位移和孔隙压力场使用线性等阶插值，与其他方法相比，这对于代码开发和维护都更直接。利用离散极大值原理，推导出合适的稳定参数，有效地保证了在一维情况下的单调性和理论上的最优性。该方法的一个吸引人的特点是稳定参数仅根据多孔材料的性质进行评估，而不涉及网格或时间步长。通过数值模拟与分析基准的比较，验证了所提出的稳定方案的有效性。
Finite element solutions of poromechanical problems often exhibit oscillating pore pressures in the limits of low permeability, fast loading rates, coarse meshes, and/or small time step sizes. To suppress completely the pore pressure oscillations, a stabilized finite element scheme with a better performance on monotonicity is proposed for modeling compressible fluid‐saturated porous media. This method, based on the polynomial pressure projection technique, allows the use of linear equal‐order interpolation for both displacement and pore pressure fields, which is more straightforward for both code development and maintenance compared to others. By employing the discrete maximum principle, a proper stabilization parameter is deduced, which is efficient to guarantee the monotonicity and optimal in theory in the 1‐dimensional case. An appealing feature of the method is that the stabilization parameter is evaluated in terms of the properties of porous material only, while no mesh or time step size is involved. Through comparing the numerical simulations with the analytical benchmarks, the efficiency of the proposed stabilization scheme is confirmed.