@Article{AAMM-14-5,
author = {Muhammad, Mohebujjaman},
title = {High Order Efficient Algorithm for Computation of MHD Flow Ensembles},
journal = {Advances in Applied Mathematics and Mechanics},
year = {2022},
volume = {14},
number = {5},
pages = {1111--1137},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {2075-1354},
doi = {https://doi.org/10.4208/aamm.OA-2021-0154},
url = {https://global-sci.com/article/72934/high-order-efficient-algorithm-for-computation-of-mhd-flow-ensembles}
}