Time-Discretization Schemes in Solving a Heat Diffusion Model
FVM Implementation
Palavras-chave:
Time-discretization, Heat diffusion model, Finite volume method, Numerical methods, Differential equationsResumo
This work proposes to analyze time-discretization schemes to solve a heat diffusion model. The latter is represented by a two-dimensional unsteady-state heat diffusion equation. The differential equation is solved using the finite volume method (FVM). The explicit method, Crank-Nicholson method, and fully implicit method are considered. The work concludes that the explicit and Crank-Nicholson methods have a maximum size for the time step, while the fully implicit method does not have this limitation but is first-order accurate. This work is an initial step in investigating higher-order schemes for more accurate solutions in complex problems.
Downloads
Referências
M. Z. Akhter, A. R. Ali, H. K. Jawahar, F. K. Omar, and E. Elnajjar. “Enhanced energy extraction in small-scale wind turbines through slot-based passive blowing”. en. In: Energy Conversion and Management: X 19 (2023), p. 100400. doi: 10.1016/j.ecmx.2023.100400.
A. Fortuna. Técnicas computacionais para dinâmica dos fluidos. 2nd ed. São Paulo: Editora da Universidade de São Paulo, 2012. isbn: 9788531405266.
T. D. Luz, F. G. Battisti, and A. K. Da Silva. “A numerical study of supercritical carbon dioxide as a medium for thermal energy storage applications under natural convection”. In: Numerical Heat Transfer, Part A: Applications 81.3-6 (2022), pp. 49–71. doi: 10.1080/10407782.2021.1969812.
C. R. Maliska. Transferência de calor e mecânica dos fluidos computacional. 2nd ed. Rio de Janeiro: LTC, 2004. isbn: 9788521613961.
H. K. Versteeg and W. Malalasekera. An introduction to computational fluid dynamics: the finite volume method. 2nd ed. Londres, Reino Unido: Pearson Education, 2007. isbn: 978-0131274983.
