Multigrid hysteretic heat diffusion
Keywords:
non-linear heat diffusion, multigrid technique, hysteresisAbstract
In this paper a transient non-linear heat diffusion problem is studied. Considering hysteretic type temperature-dependence of thermal diffusion, the numerical solution is very resource- and time-consuming. Utilizing the advantages of the multigrid technique a coarse level iterating algorithm is introduced. Applying a hierarchical algorithm the solution time could be reduced. The proposed method has been verified by comparing to other numerical schemes. The thermal heating-cooling asymmetry resulted by the hysteresis and the memory character of diffusivity are proved by numerical simulations.
References
Dai, W., Woodward, P., (1998). Numerical Simulation for Nonlinear Heat Transfer in a System of Multimaterials. In: J. Comp. Phys. 139(1), 58–78. https://doi.org/10.1006/jcph.1997.5863
González-Fernández, C. F., Alhama, F., Alarcón, M., López-Sánchez, J. F. (1998). Digital simulation of transient heat conduction with polynomial variable thermal conductivity and specific heat. In: Comp. Phys. Comm., 111(1–3), 53–58. https://doi.org/10.1016/S0010-4655(98)00026-5
Hackbusch, W. (1985). Multigrid Methods and Applications, Springer, Berlin. https://doi.org/10.1007/978-3-662-02427-0
Iványi, A. (1997). Hysteresis models in electromagnetic computation. Budapest : Akadémiai Kiadó
Kashiwada, Y., Fujishiro, H., Ibeke, M. (2003). Thermal conductivity of Pr0.65(Ca1-z Srz)0.35MnO3 under applied field. Physica B. 329–333, 924–925. https://doi.org/10.1016/S0921-4526(02)02604-2
Santos, W. N., Baldo, J. B., Taylor, R. (2000). Effect of SiC on the thermal diffusivity of silica-based materials. In: Material Research Bulletin. 35(13), 2091–2100. https://doi.org/10.1016/S0025-5408(00)00428-1
Stojan, G., Takó, G. (1995). “Numerical methods”, (in Hungarian) ELTE. Budapest.
Wawryk, R., Marucha, Cz., Balcerek, K., Terzijska, B. M., Ivanova, Z., (2000). Thermal Conductivity of polycrystalline and amorphous Se-Te-Cu system. In: Cyrogenics. 40(11), 749–752. https://doi.org/10.1016/S0011-2275(01)00032-7
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Copyright (c) 2006 Jancskárné Anweiler Ildikó, Iványi Amália

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