An efficient, partitioned ensemble algorithm for simulating ensembles of evolutionary MHD flows at low magnetic Reynolds number

摘要

Studying the propagation of uncertainties in a nonlinear dynamical systemusually involves generating a set of samples in the stochastic parameter spaceand then repeated simulations with different sampled parameters. The maindifficulty faced in the process is the excessive computational cost. In thispaper, we present an efficient, partitioned ensemble algorithm to determinemultiple realizations of a reduced Magnetohydrodynamics (MHD) system, whichmodels MHD flows at low magnetic Reynolds number. The algorithm decouples thefully coupled problem into two smaller sub-physics problems, which reduces thesize of the linear systems that to be solved and allows the use of optimizedcodes for each sub-physics problem. Moreover, the resulting coefficientmatrices are the same for all realizations at each time step, which allowsfaster computation of all realizations and significant savings in computationalcost. We prove this algorithm is first order accurate and long time stableunder a time step condition. Numerical examples are provided to verify thetheoretical results and demonstrate the efficiency of the algorithm.