CONVERGENCE ANALYSIS OF THE UZAWA ITERATIVE METHOD FOR THE THERMALLY COUPLED STATIONARY INCOMPRESSIBLE MAGNETOHYDRODYNAMICS FLOW

Aytura Keram; Pengzhan Huang

doi:10.11948/20240292

2025 Volume 15 Issue 3

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Aytura Keram, Pengzhan Huang. CONVERGENCE ANALYSIS OF THE UZAWA ITERATIVE METHOD FOR THE THERMALLY COUPLED STATIONARY INCOMPRESSIBLE MAGNETOHYDRODYNAMICS FLOW[J]. Journal of Applied Analysis & Computation, 2025, 15(3): 1563-1579. doi: 10.11948/20240292

Citation:

Aytura Keram, Pengzhan Huang. CONVERGENCE ANALYSIS OF THE UZAWA ITERATIVE METHOD FOR THE THERMALLY COUPLED STATIONARY INCOMPRESSIBLE MAGNETOHYDRODYNAMICS FLOW[J]. Journal of Applied Analysis & Computation, 2025, 15(3): 1563-1579. doi: 10.11948/20240292

CONVERGENCE ANALYSIS OF THE UZAWA ITERATIVE METHOD FOR THE THERMALLY COUPLED STATIONARY INCOMPRESSIBLE MAGNETOHYDRODYNAMICS FLOW

Aytura Keram^1,,
Pengzhan Huang^1, ,

1.
College of Mathematics and System Sciences, Xinjiang University, Urumqi 830017, China

Author Bio: Email: ayturakeram@sina.com(A. Keram)
Corresponding author: Email: hpzh@xju.edu.cn(P. Huang)
Fund Project: This work is supported by the Natural Science Foundation of Xinjiang Uygur Autonomous Region (grant number 2023D14014) and Tianshan Talent Training Program of Xinjiang Uygur Autonomous Region (grant number 2023TSYCCX0103)

Abstract

Abstract

In this paper, we designed an Uzawa iterative method for solving the thermally coupled stationary incompressible magnetohydrodynamics system, where a decoupled discrete system is obtained and no saddle point problem is required to deal with at each iterative step except the initial guess. Then, the convergence analysis of the presented method is provided. Finally, the effectiveness of the proposed method is illustrated with some numerical examples.
- Uzawa iterative method /
- thermally coupled magnetohydrodynamics /
- relaxation parameter /
- convergence analysis
MSC: 65N30, 65N12

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References

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