scholarly journals Cell boundary element methods for convection-diffusion equations

2006 ◽  
Vol 5 (2) ◽  
pp. 309-319 ◽  
Author(s):  
Youngmok Jeon ◽  
◽  
Eun-Jae Park ◽  
Keyword(s):  
Boundary Element ◽  
Boundary Element Methods ◽  
Diffusion Equations ◽  
Cell Boundary ◽  
Convection Diffusion

Weighted Finite Difference and Boundary Element Methods Applied to Groundwater Pollution Problems

1991 ◽  
Vol 23 (1-3) ◽  
pp. 517-524
Author(s):  
M. Kanoh ◽  
T. Kuroki ◽  
K. Fujino ◽  
T. Ueda
Keyword(s):  
Boundary Element Method ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Boundary Element ◽  
Difference Method ◽  
Groundwater Pollution ◽  
Small Region ◽  
Boundary Element Methods ◽  
Computational Time ◽  
Element Method

The purpose of the paper is to apply two methods to groundwater pollution in porous media. The methods are the weighted finite difference method and the boundary element method, which were proposed or developed by Kanoh et al. (1986,1988) for advective diffusion problems. Numerical modeling of groundwater pollution is also investigated in this paper. By subdividing the domain into subdomains, the nonlinearity is localized to a small region. Computational time for groundwater pollution problems can be saved by the boundary element method; accurate numerical results can be obtained by the weighted finite difference method. The computational solutions to the problem of seawater intrusion into coastal aquifers are compared with experimental results.

scholarly journals Discrete effect on single-node boundary schemes of lattice Bhatnagar–Gross–Krook model for convection-diffusion equations

2019 ◽  
Vol 31 (01) ◽  
pp. 2050017
Author(s):  
Liang Wang ◽  
Xuhui Meng ◽  
Hao-Chi Wu ◽  
Tian-Hu Wang ◽  
Gui Lu
Keyword(s):  
Boundary Condition ◽  
Relaxation Time ◽  
Lattice Boltzmann ◽  
Diffusion Equations ◽  
Bgk Model ◽  
Distance Ratio ◽  
Single Node ◽  
Convection Diffusion ◽  
Velocity Models ◽  
Discrete Effect

The discrete effect on the boundary condition has been a fundamental topic for the lattice Boltzmann method (LBM) in simulating heat and mass transfer problems. In previous works based on the anti-bounce-back (ABB) boundary condition for convection-diffusion equations (CDEs), it is indicated that the discrete effect cannot be commonly removed in the Bhatnagar–Gross–Krook (BGK) model except for a special value of relaxation time. Targeting this point in this paper, we still proceed within the framework of BGK model for two-dimensional CDEs, and analyze the discrete effect on a non-halfway single-node boundary condition which incorporates the effect of the distance ratio. By analyzing an unidirectional diffusion problem with a parabolic distribution, the theoretical derivations with three different discrete velocity models show that the numerical slip is a combined function of the relaxation time and the distance ratio. Different from previous works, we definitely find that the relaxation time can be freely adjusted by the distance ratio in a proper range to eliminate the numerical slip. Some numerical simulations are carried out to validate the theoretical derivations, and the numerical results for the cases of straight and curved boundaries confirm our theoretical analysis. Finally, it should be noted that the present analysis can be extended from the BGK model to other lattice Boltzmann (LB) collision models for CDEs, which can broaden the parameter range of the relaxation time to approach 0.5.

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