Second Order, Unconditionally Stable, Linear Ensemble Algorithms for the Magnetohydrodynamics Equations

We propose two unconditionally stable, linear ensemble algorithms with pre-computable shared coefficient matrices across different realizations for the magnetohydrodynamics equations. The viscous terms are treated by a standard perturbative discretization. The nonlinear terms are discretized fully explicitly within the framework of the generalized positive auxiliary variable approach (GPAV). Artificial viscosity stabilization that modifies the kinetic energy is introduced to improve accuracy of the GPAV ensemble methods. Numerical results are presented to demonstrate the accuracy and robustness of the ensemble algorithms.