Numerical Analysis of a Second Order Ensemble Method for Evolutionary Magnetohydrodynamics Equations at Small Magnetic Reynolds Number


We study a second order ensemble method for fast computation of an ensemble of magnetohydrodynamics flows at small magnetic Reynolds number. Computing an ensemble of flow equations with different input parameters is a common procedure for uncertainty quantification in many engineering applications, for which the computational cost can be prohibitively expensive for nonlinear complex systems. We propose an ensemble algorithm that requires only solving one linear system with multiple right-hands instead of solving multiple different linear systems, which significantly reduces the computational cost and simulation time. Comprehensive stability and error analyses are presented proving conditional stability and second order in time convergent. Numerical tests are provided to illustrate theoretical results and demonstrate the efficiency of the proposed algorithm.


Mathematics and Statistics


John Carter was partially supported by the US National Science Foundation, Grant/Award Number: DMS-1720001. Nan Jiang was partially supported by the US National Science Foundation, Grant/Award Number: DMS-1720001 and DMS-2120413.

Keywords and Phrases

Ensemble Algorithm; Finite Element Method; Low Magnetic Reynolds Number; MHD; Partitioned Method; Uncertainty Quantification

International Standard Serial Number (ISSN)

1098-2426; 0749-159X

Document Type

Article - Journal

Document Version


File Type





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Publication Date

01 Sep 2022