A numerical method for two-dimensional transient nonlinear convection-diffusion equations

• Published in: Annals of nuclear energy 2024-09, Vol.205, p.110604, Article 110604
• Main Authors: Meng, Xiangyuan, Huang, Mei, Wang, Boxue, Ouyang, Xiaoping, Huang, Yanping, Chen, Denggao, Cheng, Yanting, Li, Yaodi
• Format: Article
• Language: English
• Subjects: Burgers’ equation; Convection domination; Half boundary method; Nonlinear; Variable coefficients
• ISSN: 0306-4549; 1873-2100
• DOI: 10.1016/j.anucene.2024.110604

•The HBM can reduce maximum matrix order and optimizate memory storage.•The numerical results demonstrate the method’s potential in situations where convection is dominant.•The HBM exhibits numerical capabilities in predicting the dispersion levels of radioactive nuclides. In this research, we have developed the half-boundary method (HBM) for nonlinear convection-diffusion equations (CDEs), which hold significant importance in nuclear power engineering. The HBM employs a variable relationship between the nodes within the computational domain and the nodes located on half of the boundaries. This approach offers notable benefits, includingthe reduction ofthe maximum matrix order and the optimization the maximum memory storage for calculations. Moreover, the HBM is an efficient and streamlined approach to directly handle Neumann boundary conditions, thanks to the utilization of mixed variables. We primarily investigate the memory usage and accuracy of the proposed algorithm in the unsteady-state CDEs, in context of material nonlinear CDEs, the Burgers’ equation and the system of Burgers' equations. The numerical results obtained demonstrate the method’s potential in simulating flow and heat transfer phenomena, particularly in situations where convection is dominant.