参数化MHD流问题集合模拟的一种有效算法
An efficient algorithm for simulating ensembles of parameterized MHD flow problems
摘要：
在本文中，我们提出，分析和测试一个有效的算法计算不可压缩磁流体动力学（MHD）流的系综平均值，其中实例/成员对应于不同的运动粘度，磁扩散率，体力，和初始条件。该算法是解耦的Elsässer变量，并允许在每个时间步的所有成员共享的系数矩阵。因此，该算法是更有效的计算比单独计算模拟每个成员使用通常的MHD算法。我们证明了该算法是无条件稳定和收敛的。几个数值试验，以支持预测的收敛速度。最后，我们测试所提出的计划，并观察如何的物理行为的变化，作为耦合数的增加，在盖子驱动的空腔问题的平均雷诺数$Re\approx 15000$，并作为偏差的不确定性的初始和边界条件的增加，在通道流通过一个台阶问题。
英文摘要：
In this paper, we propose, analyze, and test an efficient algorithm for computing ensemble average of incompressible magnetohydrodynamics (MHD) flows, where instances/members correspond to varying kinematic viscosity, magnetic diffusivity, body forces, and initial conditions. The algorithm is decoupled in Elsässer variables and permits a shared coefficient matrix for all members at each time-step. Thus, the algorithm is much more computationally efficient than separately computing simulations for each member using usual MHD algorithms. We prove the proposed algorithm is unconditionally stable and convergent. Several numerical tests are given to support the predicted convergence rates. Finally, we test the proposed scheme and observe how the physical behavior changes as the coupling number increases in a lid-driven cavity problem with mean Reynolds number $Re\approx 15000$, and as the deviation of uncertainties in the initial and boundary conditions increases in a channel flow past a step problem.
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