一种高效的分区群体算法用于模拟低磁雷诺数下的流体磁动力学群体
An efficient, partitioned ensemble algorithm for simulating ensembles of evolutionary MHD flows at low magnetic Reynolds number
AI总结：
本文提出一种高效算法，通过分解问题减少计算成本，用于模拟低磁雷诺数下的流体磁动力学群体，证明其一阶精度和长时间稳定性。
摘要：
研究非线性动力系统中不确定性传播通常涉及在随机参数空间中生成样本并进行多次模拟。主要困难在于计算成本过高。本文提出一种高效的分区群体算法，用于确定减少的磁流体动力学（MHD）系统的多个实现。该算法将完全耦合的问题分解为两个较小的子物理问题，从而减少需要求解的线性系统规模，并允许为每个子物理问题使用优化代码。此外，所得到的系数矩阵在每个时间步长对所有实现都相同，这允许更快地计算所有实现并显著节省计算成本。我们证明该算法在时间步长条件下具有第一阶精度和长时间稳定性。数值示例用于验证理论结果并展示算法的效率。
英文摘要：
Studying the propagation of uncertainties in a nonlinear dynamical system usually involves generating a set of samples in the stochastic parameter space and then repeated simulations with different sampled parameters. The main difficulty faced in the process is the excessive computational cost. In this paper, we present an efficient, partitioned ensemble algorithm to determine multiple realizations of a reduced Magnetohydrodynamics (MHD) system, which models MHD flows at low magnetic Reynolds number. The algorithm decouples the fully coupled problem into two smaller sub-physics problems, which reduces the size of the linear systems that to be solved and allows the use of optimized codes for each sub-physics problem. Moreover, the resulting coefficient matrices are the same for all realizations at each time step, which allows faster computation of all realizations and significant savings in computational cost. We prove this algorithm is first order accurate and long time stable under a time step condition. Numerical examples are provided to verify the theoretical results and demonstrate the efficiency of the algorithm.
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