Uncertainty quantification of the gem challenge magnetic reconnection problem using the multilevel Monte Carlo method

Abstract

Plasma modelers often change the ion-to-electron mass ratio and speed of light to Alfvén speed ratio to decrease computational cost. Changing these parameters may affect the outcome of simulation and uncertainty in the results. This work aims to quantify the uncertainty of varying the ion-to-electron mass ratio, speed of light to Alfvén speed ratio, and the initial magnetic flux perturbation on the reconnected flux to provide a confidence limit. In this study, the multilevel Monte Carlo (MMC) method is employed to estimate the mean and variance, and the results are compared with the standard Monte Carlo (MC) and the probabilistic collocation (PC) methods. The plasma model used here is the two-fluid plasma where ions and electrons are treated as two separate fluids. Numerical simulations are presented showing the effectiveness of the MMC method when applied to the quasi-neutral ion cyclotron waves and the Geospace Environment Modeling (GEM) magnetic reconnection challenge problems. The mean reconnected flux with error bars provides a reconnection flux variation envelope, which can help numerical modelers to evaluate whether their reconnection flux lies inside the envelope for different plasma models. The results of the MMC mean and variance are comparable to the MC method but at a much lower computational cost.