convection diffusion
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2022 ◽  
Vol 201 ◽  
pp. 103703
Author(s):  
Luis Blanco-Cocom ◽  
Salvador Botello-Rionda ◽  
L.C. Ordoñez ◽  
S. Ivvan Valdez

2022 ◽  
Vol 135 ◽  
pp. 322-336
Author(s):  
Yuanyuan Zhao ◽  
Mei Huang ◽  
Xiaoping Ouyang ◽  
Jun Luo ◽  
Yongqing Shen ◽  
...  

Mathematics ◽  
2022 ◽  
Vol 10 (2) ◽  
pp. 188
Author(s):  
Jen-Yi Chang ◽  
Ru-Yun Chen ◽  
Chia-Cheng Tsai

This article describes the development of the Hermite method of approximate particular solutions (MAPS) to solve time-dependent convection-diffusion-reaction problems. Using the Crank-Nicholson or the Adams-Moulton method, the time-dependent convection-diffusion-reaction problem is converted into time-independent convection-diffusion-reaction problems for consequent time steps. At each time step, the source term of the time-independent convection-diffusion-reaction problem is approximated by the multiquadric (MQ) particular solution of the biharmonic operator. This is inspired by the Hermite radial basis function collocation method (RBFCM) and traditional MAPS. Therefore, the resultant system matrix is symmetric. Comparisons are made for the solutions of the traditional/Hermite MAPS and RBFCM. The results demonstrate that the Hermite MAPS is the most accurate and stable one for the shape parameter. Finally, the proposed method is applied for solving a nonlinear time-dependent convection-diffusion-reaction problem.


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