Numerical Algorithms for Identification of Convection Coefficient and Source in a Magnetohydrodynamics Flow
Abstract
:1. Introduction
2. Formulation of the Direct and Inverse Problems
2.1. The Direct Problem
2.2. The Inverse Problems
3. Reduction of the IP1, IP2, and IP3 to Nonclassical Problems
4. Well-Posedness of the Inverse Problems
4.1. The IP2
4.2. The IP1 and IP3
5. Finite Difference Approximation of the Inverse Problems
6. Algorithms for Solution of Finite Difference Algebraic Systems
6.1. The IP2
6.2. The IP3 and IP1
7. Computational Results
7.1. Inverse Problem without Noise
7.2. Inverse Problem with a Noise
8. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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u | B | f | ||||||||
---|---|---|---|---|---|---|---|---|---|---|
Ratio | Order | Ratio | Order | Ratio | Order | |||||
5 | 5 | 9.2310e-03 | - | - | 6.5473e-04 | - | - | 1.1485e-02 | ||
10 | 10 | 5.0943e-03 | 1.81 | 0.86 | 1.6591e-04 | 3.95 | 1.98 | 6.1159e-03 | 1.88 | 0.91 |
20 | 20 | 2.6823e-03 | 1.90 | 0.93 | 4.5833e-05 | 3.60 | 1.85 | 3.1974e-03 | 1.91 | 0.94 |
40 | 40 | 1.3803e-03 | 1.94 | 0.96 | 1.6712e-05 | 2.72 | 1.45 | 1.6416e-03 | 1.95 | 0.96 |
80 | 80 | 7.0073e-04 | 1.97 | 0.98 | 7.1775e-06 | 2.32 | 1.21 | 8.3274e-04 | 1.97 | 0.98 |
160 | 160 | 3.5312e-04 | 1.98 | 0.99 | 3.3274e-06 | 2.14 | 1.11 | 4.1952e-04 | 1.99 | 0.99 |
ffl | 0 | 0.0005 | 0.001 | 0.01 | 0.1 |
---|---|---|---|---|---|
u | 1.3803e-03 | 1.3638e-03 | 1.5238e-03 | 2.1379e-03 | 1.6747e-02 |
B | 1.6712e-05 | 1.6546e-05 | 1.6297e-05 | 2.5556e-05 | 1.6864e-04 |
f | 1.6416e-03 | 1.8412e-03 | 1.9766e-03 | 7.8766e-03 | 6.8009e-02 |
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Kandilarov, J.D.; Vulkov, L.G. Numerical Algorithms for Identification of Convection Coefficient and Source in a Magnetohydrodynamics Flow. Algorithms 2024, 17, 387. https://doi.org/10.3390/a17090387
Kandilarov JD, Vulkov LG. Numerical Algorithms for Identification of Convection Coefficient and Source in a Magnetohydrodynamics Flow. Algorithms. 2024; 17(9):387. https://doi.org/10.3390/a17090387
Chicago/Turabian StyleKandilarov, Juri D., and Lubin G. Vulkov. 2024. "Numerical Algorithms for Identification of Convection Coefficient and Source in a Magnetohydrodynamics Flow" Algorithms 17, no. 9: 387. https://doi.org/10.3390/a17090387