Year: 2022
Author: Muhammad Mohebujjaman
Advances in Applied Mathematics and Mechanics, Vol. 14 (2022), Iss. 5 : pp. 1111–1137
Abstract
In this paper, we propose, analyze, and test a new fully discrete, efficient, decoupled, stable, and practically second-order time-stepping algorithm for computing MHD ensemble flow averages under uncertainties in the initial conditions and forcing. For each viscosity and magnetic diffusivity pair, the algorithm picks the largest possible parameter $θ ∈ [0,1]$ to avoid the instability that arises due to the presence of some explicit viscous terms. At each time step, the algorithm shares the same system matrix with all $J$ realizations but has different right-hand-side vectors for all $J$ realizations. This saves assembling time and computer memory, allows the reuse of the same preconditioner, and can take the advantage of block linear solvers. For the proposed algorithm, we prove stability and convergence rigorously. To illustrate the predicted convergence rates of our analysis, numerical experiments with manufactured solutions are given on a unit square domain. Finally, we test the scheme on a benchmark channel flow over a step problem and it performs well.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2021-0154
Advances in Applied Mathematics and Mechanics, Vol. 14 (2022), Iss. 5 : pp. 1111–1137
Published online: 2022-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 27
Keywords: Magnetohydrodynamics uncertainty quantification fast ensemble calculation finite element method Elsässer variables second rder scheme.
Author Details
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