非线性渗透率弱耦合孔隙弹性问题的解耦线性化离散方法
A decoupling and linearizing discretization for weakly coupled poroelasticity with nonlinear permeability
摘要：
在弹性模型与渗流方程弱耦合的条件下，分析了具有非线性渗透率的孔隙弹性问题的一阶半显式时间离散格式。该方法导致方程的解耦，同时，线性化的非线性，而不需要进一步的内迭代步骤。因此，计算速度提高了两倍，而不会损失收敛速度。我们证明了最佳的一阶误差估计，考虑相关的延迟系统，并探讨了不同的例子与各种类型的非线性位移-渗透率关系的数值方法。
英文摘要：
We analyze a semi-explicit time discretization scheme of first order for poro\-elasticity with nonlinear permeability provided that the elasticity model and the flow equation are only weakly coupled. The approach leads to a decoupling of the equations and, at the same time, linearizes the nonlinearity without the need of further inner iteration steps. Hence, the computational speed-up is twofold without a loss in the convergence rate. We prove optimal first-order error estimates by considering a related delay system and investigate the method numerically for different examples with various types of nonlinear displacement-permeability relations.
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