An efficient, partitioned ensemble algorithm for simulating ensembles of evolutionary MHD flows at low magnetic Reynolds number
For researchers studying uncertainty propagation in MHD flows, this algorithm offers a computationally cheaper way to run ensemble simulations, though it is an incremental improvement over existing methods.
This paper presents a partitioned ensemble algorithm for simulating ensembles of evolutionary MHD flows at low magnetic Reynolds number, which reduces computational cost by decoupling the problem into two smaller sub-physics problems and reusing coefficient matrices across realizations. The algorithm is proven first-order accurate and long-time stable, with numerical examples verifying its efficiency.
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.