Stability of multirate explicit coupling of geomechanics with flow in a poroelastic medium
Stability of multirate explicit coupling of geomechanics with flow in a poroelastic medium
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多孔弹性介质中地质力学与流动多速率显式耦合的稳定性
DOI：
10.1016/j.camwa.2019.04.007
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发表时间：
2019
期刊：
影响因子：
--
通讯作者：
M. Wheeler
中科院分区：
文献类型：
--
作者：
T. Almani;Kundan Kumar;Gurpreet Singh;M. Wheeler
我们考虑了用于模拟多孔弹性介质中耦合流动和地质力学的毕奥系统的单速率和多速率显式方案。这些方案在实践中被广泛使用，遵循一个顺序的程序，其中流动和力学问题是完全解耦的。在这样的方案中，首先解决流动问题，并滞后位移项，然后解决力学问题。多速率显式耦合方案利用不同的时间尺度的力学和流动问题，采取多个精细的时间步长内流动一个粗糙的力学时间步长。我们提供了完全离散计划的单和多速率的方法，使用向后欧拉时间离散和混合空间的流动和共形Galerkin力学。我们进行了严格的稳定性分析，并推导出条件的水库参数和数量的更精细的流解决方案，以确保两个计划的稳定性。此外，我们调查的计算时间节省显式耦合方案对迭代耦合方案。
We consider single rate and multirate explicit schemes for the Biot system modeling coupled flow and geomechanics in a poro-elastic medium. These schemes are widely used in practice that follows a sequential procedure in which the flow and mechanics problems are fully decoupled. In such a scheme, the flow problem is solved first with time-lagging the displacement term followed by the mechanics solve. The multirate explicit coupling scheme exploits the different time scales for the mechanics and flow problems by taking multiple finer time steps for flow within one coarse mechanics time step. We provide fully discrete schemes for both the single and multirate approaches that use Backward Euler time discretization and mixed spaces for flow and conformal Galerkin for mechanics. We perform a rigorous stability analysis and derive the conditions on reservoir parameters and the number of finer flow solves to ensure stability for both schemes. Furthermore, we investigate the computational time savings for explicit coupling schemes against iterative coupling schemes.