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

TL;DR

This paper introduces an efficient partitioned ensemble algorithm for simulating multiple realizations of low magnetic Reynolds number MHD flows, significantly reducing computational costs while maintaining accuracy and stability.

Contribution

The paper presents a novel partitioned ensemble algorithm that decouples the MHD system into smaller problems, enabling faster computation of multiple realizations with shared matrices.

Findings

Algorithm is first order accurate.

Algorithm is long time stable under certain conditions.

Numerical examples confirm efficiency and theoretical results.

Abstract

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.