Second order, unconditionally stable, linear ensemble algorithms for the magnetohydrodynamics equations

TL;DR

This paper introduces two unconditionally stable, linear ensemble algorithms for magnetohydrodynamics equations that are efficient, accurate, and robust, utilizing shared coefficient matrices and explicit nonlinear discretization.

Contribution

The paper presents novel unconditionally stable, linear ensemble algorithms with shared matrices and explicit nonlinear treatment for MHD equations, enhancing computational efficiency and stability.

Findings

Algorithms are unconditionally stable and linear.

Numerical results confirm accuracy and robustness.

Artificial viscosity improves energy stability.

Abstract

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.