Hyperbolic PDE models for dynamo-type magnetic field behaviour
Swapnali Makdeyswapnali@frcrce.ac.inDepartment of Electronics and Computer ScienceFr. Conceicao Rodrigues College of EngineeringUniversity of MumbaiMumbai, Maharashtra, 400050, IndiaView full profile → , Avinash B. Rautavinash.raut@vit.eduDepartment of Engineering Science and HumanitiesVishwakarma Institute of TechnologyPune, Maharashtra, 411037, India0000-0002-7870-8223View full profile → , Mahadev N. Chougulemahadevchougule@gmail.comDepartment of Electrical EngineeringSinhgad Institute of Technology & ScienceNarhe, Pune, Maharashtra, 411041, IndiaView full profile → , Machindranath B. Diwatediwatemachindra@gmail.comDepartment of MathematicsSinhgad Institute of Technology & ScienceNarhe, Pune, Maharashtra, 411041, IndiaView full profile → , Vijaya Sagvekarvijaya.s@xavier.ac.inDepartment of Computer Science and EngineeringXavier Institute of EngineeringUniversity of MumbaiMumbai, Maharashtra, 400016, IndiaView full profile → , *Ninad MoreCorresponding authorninadmoree@gmail.comDepartment of Computer Science and EngineeringXavier Institute of EngineeringUniversity of MumbaiMumbai, Maharashtra, 400016, IndiaView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 01 Apr 2026
- Published Online:
- 27 Oct 2026
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JIM-2810
- Pages:
- 3269–3280
Abstract
By introducing finite propagation speeds and wave-like magnetic transport effects, hyperbolic partial differential equation (PDE) models are very useful in describing the behaviour of the magnetic field of dynamo type as it passes through an electrically conducting medium. In this study, we have created a hyperbolic dynamo model using the conservation principles and magnetohydrodynamic theory to study the evolution of the magnetic field under transient conditions. This is done by using stable numerical algorithms in both space and time for the governing equations and by using an efficient computational algorithm to accurately simulate them. The proposed methodology is able to more realistically represent magnetic induction, diffusion and propagation phenomena than classical parabolic formulations. Stabilization, decrease in numerical dispersion and prediction of transient magnetic structures is proven with numerical results. The framework developed is a framework that is mathematically sound which can be used for the analysis of astrophysical, geophysical and engineering dynamo systems and can be used as a mathematical tool in future studies of more complex dynamo systems in astrophysics, geophysics and engineering.
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References
[1] O. Sheremetyeva, “Magnetic field dynamical regimes in a large-scale low-mode αΩ-dynamo model with hereditary α-quenching by field energy,” Mathematics, vol. 11, no. 10, Art. no. 2297 (2023), doi: 10.3390/math11102297.
[2] E. Kazakov, G. Vodinchar, and D. Tverdyi, “Two-mode hereditary model of solar dynamo,” Mathematics, vol. 13, no. 10, Art. no. 1669 (2025), doi: 10.3390/math13101669.
[3] E. Mikhailov, D. Boneva, and M. Pashentseva, “No-z model for magnetic fields of different astrophysical objects and stability of the solutions,” Data, vol. 6, no. 1, Art. no. 4 (2021), doi: 10.3390/data6010004.
[4] J. V. Shebalin, “Magnetohyrodynamic turbulence in a spherical shell: Galerkin models, boundary conditions, and the dynamo problem,” Fluids, vol. 10, no. 2, Art. no. 24 (2025), doi: 10.3390/fluids10020024.
[5] D. J. Williams, M. Ivanov, and C. Ferreira, “A systematic review of hyperbolic PDE models for dynamo-type magnetic field behaviour: Methods, architectures, and future research directions,” Int. J. Electr., Electron. Comput. Syst., vol. 14, no. 2, pp. 140–150 (2025), doi: 10.65521/ijeecs.v14i2.2109.
[6] A. T. Clarke, C. J. Davies, D. Ruprecht, and S. M. Tobias, “Parallel-in-time integration of kinematic dynamos,” J. Comput. Phys. X, vol. 7, Art. no. 100057 (2020), doi: 10.1016/j.jcpx.2020.100057.
[7] M. A. Shay, S. Adhikari, N. Beesho, J. Birn, J. Büchner, P. Cassak, L.-J. Chen, Y. Chen, G. Cozzani, J. Drake, F. Guo, M. Hesse, N. Jain, Y. Pfau-Kempf, Y. Lin, Y.-H. Liu, M. Oka, Y. Omelchenko, M. Palmroth, O. Pezzi, P. H. Reiff, M. Swisdak, F. Toffoletto, G. Tóth, and R. A. Wolf, “Simulation Models for Exploring Magnetic Reconnection,” Space Science Reviews, vol. 221, no. 6, Art. no. 81 (2025), doi: 10.1007/s11214-025-01210-5.
[8] A. Jhangeer and Beenish, “Study of magnetic fields using dynamical patterns and sensitivity analysis,” Chaos Solitons Fractals, vol. 182, Art. no. 114827 (2024), doi: 10.1016/j.chaos.2024.114827.
[9] R. Keppens, J. Teunissen, C. Xia, and O. Porth, “MPI-AMRVAC: A parallel, grid-adaptive PDE toolkit,” Comput. Math. Appl., vol. 81, pp. 316–333 (2021), doi: 10.1016/j.camwa.2020.03.023.
[10] A. Calvo-Fernández, M. Blanco-Rey, and A. Eiguren, “Numerical renormalization group calculations for magnetic impurity systems with spin-orbit coupling and crystal-field effects,” Comput. Phys. Commun., vol. 312, Art. no. 109613 (2025), doi: 10.1016/j.cpc.2025.109613.
[11] A. Jhangeer, A. R. Ansari, M. Imran, Beenish, and M. B. Riaz, “Conserved quantities and sensitivity analysis influence of damping effect in ferrites materials,” Alexandria Eng. J., vol. 86, pp. 298–310 (2024), doi: 10.1016/j.aej.2023.11.067.
[12] H. Almusawa, A. Jhangeer, and Beenish, “Soliton solutions, Lie symmetry analysis and conservation laws of ionic waves traveling through microtubules in live cells,” Results Phys., vol. 43, Art. no. 106028 (2022), doi: 10.1016/j.rinp.2022.106028.
[13] O. V. Sheremetyeva and A. N. Godomskaya, “Modelling the magnetic field generation modes in the low-mode model of the αΩ-dynamo with varying intensity of the α-effect,” Vestn. Yuzhno-Ural. Gos. Univ. Ser. Mat. Model. Program., vol. 14, no. 2, pp. 27–38 (2021), doi: 10.14529/mmp210203.
[14] C. Deshpande, C. Ramtirthkar, T. A. Wani, V. K. Bhosale, M. Gulhane, and K. S. Kumar, “Topology and knot theory applications in quantum field theory,” Journal of Interdisciplinary Mathematics, vol. 28, no. 6, pp. 2281–2287 (2025), doi: 10.47974/JIM-2370.
