SIAM Journal on Numerical Analysis, Volume 59, Issue 1, Page 583-612, January 2021.
In this work, we consider compressible single-phase flow problems in a porous medium containing a fracture. In the fracture, a nonlinear pressure-velocity relation is prescribed. Using a non-overlapping domain decomposition procedure, we reformulate the global problem into a nonlinear interface problem. We then introduce two new algorithms that are able to efficiently handle the nonlinearity and the coupling between the fracture and the matrix, both based on linearization by the so-called L-scheme. The first algorithm, named MoLDD, uses the L-scheme to resolve for the nonlinearity, requiring at each iteration to solve the dimensional coupling via a domain decomposition approach. The second algorithm, called ItLDD, uses a sequential approach in which the dimensional coupling is part of the linearization iterations. For both algorithms, the computations are reduced only to the fracture by precomputing, in an offline phase, a multiscale flux basis (the linear Robin-to-Neumann codimensional map), that represent the flux exchange between the fracture and the matrix. We present extensive theoretical findings X and in particular, t. The stability and the convergence of both schemes are obtained, where user-given parameters are optimized to minimize the number of iterations. Examples on two important fracture models are computed with the library PorePy and agree with the developed theory.

中文翻译：

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减少非线性断裂流模型的鲁棒线性域分解方案

SIAM数值分析学报，第59卷，第1期，第583-612页，2021年1月。
在这项工作中，我们考虑了包含裂缝的多孔介质中的可压缩单相流动问题。在裂缝中，规定了非线性压力-速度关系。使用非重叠域分解过程，我们将全局问题重新构造为非线性接口问题。然后，我们介绍两种新算法，它们都可以有效地处理非线性和裂缝与基体之间的耦合，这两种算法均基于所谓的L型方案进行线性化。第一种算法称为MoLDD，它使用L方案来解决非线性问题，要求在每次迭代时都通过域分解方法来解决尺寸耦合问题。第二种算法称为ItLDD，它使用顺序方法，其中尺寸耦合是线性化迭代的一部分。对于这两种算法，通过在离线阶段预先计算多尺度通量基础（线性Robin-to-Neumann坐标图）来表示裂缝和基体之间的通量交换，从而仅将计算简化为裂缝。我们提出了广泛的理论发现X，特别是t。获得了两种方案的稳定性和收敛性，其中优化了用户提供的参数以最大程度地减少迭代次数。用库PorePy计算了两个重要断裂模型的示例，并与已开发的理论相吻合。获得了两种方案的稳定性和收敛性，其中优化了用户提供的参数以最大程度地减少迭代次数。用库PorePy计算了两个重要断裂模型的示例，并与已开发的理论相吻合。获得了两种方案的稳定性和收敛性，其中优化了用户提供的参数以最大程度地减少迭代次数。用库PorePy计算了两个重要断裂模型的示例，并与已开发的理论相吻合。