We consider the numerical behavior of the fixed-stress splitting method for coupled poromechanics as undrained regimes are approached. We explain that pressure stability is related to the splitting error of the scheme, not the fact that the discrete saddle point matrix never appears in the fixed-stress approach. This observation reconciles previous results regarding the pressure stability of the splitting method. Using examples of compositional poromechanics with application to geological CO sequestration, we see that solutions obtained using the fixed-stress scheme with a low order finite element-finite volume discretization which is not inherently inf-sup stable can exhibit the same pressure oscillations obtained with the corresponding fully implicit scheme. Moreover, pressure jump stabilization can effectively remove these spurious oscillations in the fixed-stress setting, while also improving the efficiency of the scheme in terms of the number of iterations required at every time step to reach convergence.

中文翻译：

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组合孔隙力学的压力稳定固定应力迭代解

我们考虑在接近不排水状态时耦合孔隙力学的固定应力分裂方法的数值行为。我们解释说，压力稳定性与方案的分裂误差有关，而不是离散鞍点矩阵在固定应力方法中从未出现的事实。这一观察结果与之前有关分裂方法压力稳定性的结果相一致。使用组合孔隙力学应用于地质二氧化碳封存的例子，我们看到使用具有低阶有限元有限体积离散化的固定应力方案获得的解决方案，其本质上不是 inf-sup 稳定的，可以表现出与使用以下方法获得的相同的压力振荡：相应的完全隐式方案。此外，压力跳跃稳定可以有效地消除固定应力设置中的这些寄生振荡，同时还可以提高方案在每个时间步达到收敛所需的迭代次数方面的效率。