An efficient algorithm for simulating ensembles of parameterized MHD flow problems

TL;DR

This paper introduces a computationally efficient, stable, and convergent algorithm for simulating ensembles of parameterized MHD flows, enabling faster analysis of flow variations due to physical parameter changes.

Contribution

The paper presents a novel decoupled ensemble algorithm for MHD flows that uses shared matrices, improving computational efficiency over traditional methods.

Findings

Algorithm is unconditionally stable and convergent.

Numerical tests confirm convergence rates.

Physical behavior varies with coupling number and initial condition uncertainties.

Abstract

In this paper, we propose, analyze, and test an efficient algorithm for computing ensemble average of incompressible magnetohydrodynamics (MHD) flows, where instances/members correspond to varying kinematic viscosity, magnetic diffusivity, body forces, and initial conditions. The algorithm is decoupled in Els\"asser variables and permits a shared coefficient matrix for all members at each time-step. Thus, the algorithm is much more computationally efficient than separately computing simulations for each member using usual MHD algorithms. We prove the proposed algorithm is unconditionally stable and convergent. Several numerical tests are given to support the predicted convergence rates. Finally, we test the proposed scheme and observe how the physical behavior changes as the coupling number increases in a lid-driven cavity problem with mean Reynolds number $Re\approx 15000$, and as the deviation of uncertainties in the initial and boundary conditions increases in a channel flow past a step problem.