An Efficient Algorithm for Computation of MHD Flow Ensembles
An Efficient Algorithm for Computation of MHD Flow Ensembles
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DOI：
10.1515/cmam-2016-0033
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发表时间：
2017
影响因子：
1.3
通讯作者：
M. Mohebujjaman;L. Rebholz
中科院分区：
文献类型：
--
作者：
M. Mohebujjaman;L. Rebholz
摘要提出并研究了一种计算不可压缩磁流体（MHD）流系综的有效算法。J个实现的总体平均值通过一个聪明的算法（改编自Jiang和莱顿[23]的突破性思想）来近似，该算法在每个时间步对J个系统的每个解使用相同的矩阵。因此，每个时间步长只需要构建一次预处理器，并且该算法可以利用块线性求解器。此外，Elsässer变量配方使用，它允许在每个时间步长的每个MHD系统的稳定解耦。我们证明了算法的稳定性和收敛性，并通过两个数值实验对其进行了检验。
Abstract An efficient algorithm is proposed and studied for computing flow ensembles of incompressible magnetohydrodynamic (MHD) flows under uncertainties in initial or boundary data. The ensemble average of J realizations is approximated through a clever algorithm (adapted from a breakthrough idea of Jiang and Layton [23]) that, at each time step, uses the same matrix for each of the J systems solves. Hence, preconditioners need to be built only once per time step, and the algorithm can take advantage of block linear solvers. Additionally, an Elsässer variable formulation is used, which allows for a stable decoupling of each MHD system at each time step. We prove stability and convergence of the algorithm, and test it with two numerical experiments.