An artificial compressibility ensemble algorithm for a stochastic Stokes‐Darcy model with random hydraulic conductivity and interface conditions
An artificial compressibility ensemble algorithm for a stochastic Stokes‐Darcy model with random hydraulic conductivity and interface conditions
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DOI：
10.1002/nme.6241
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发表时间：
2019-11
影响因子：
2.9
通讯作者：
Xiaoming He;N. Jiang;Changxin Qiu
中科院分区：
文献类型：
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作者：
Xiaoming He;N. Jiang;Changxin Qiu
提出并分析了一种有效的具有人工可压缩性(AC)的集成算法，用于具有随机导水率(包括界面条件)、源项和初始条件的随机Stokes-Darcy模型的多重实现的快速解耦计算。所有实现都通过求解三个较小的解耦子问题和两个公共时无关系数矩阵来找到解，这显著地提高了矩阵系统的组装和求解的效率。完全耦合的Stokes-Darcy系统可以通过分块时间推进的思想首先解耦为两个较小的子物理问题，从而减小了线性系统的规模，并允许对每个子物理问题进行并行计算。AC进一步分离了速度和压力，从而进一步减少了存储需求并提高了计算效率。我们证明了这种新的系综方法的长期稳定性和收敛性。给出了三个数值算例来支持理论结果，并说明了算法的特点，包括收敛、稳定性、效率和适用性。
We propose and analyze an efficient ensemble algorithm with artificial compressibility (AC) for fast decoupled computation of multiple realizations of the stochastic Stokes‐Darcy model with random hydraulic conductivity (including the one in the interface conditions), source terms, and initial conditions. The solutions are found by solving three smaller decoupled subproblems with two common time‐independent coefficient matrices for all realizations, which significantly improves the efficiency for both assembling and solving the matrix systems. The fully coupled Stokes‐Darcy system can be first decoupled into two smaller subphysics problems by the idea of the partitioned time stepping, which reduces the size of the linear systems and allows parallel computing for each subphysics problem. The AC further decouples the velocity and pressure which further reduces storage requirements and improves computational efficiency. We prove the long time stability and the convergence for this new ensemble method. Three numerical examples are presented to support the theoretical results and illustrate the features of the algorithm, including the convergence, stability, efficiency, and applicability.