A single-node characteristic collocation method for unsteady-state convection-diffusion equations in three-dimensional spaces

2011 ◽  
Vol 27 (4) ◽  
pp. 786-802 ◽  
Author(s):  
Li Wu ◽  
Kaixin Wang
Keyword(s):  
Collocation Method ◽  
Three Dimensional ◽  
Diffusion Equations ◽  
Unsteady State ◽  
Single Node ◽  
Convection Diffusion

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.

Universal Parallel Solver for Convection-Diffusion Equations

2004 ◽  
Vol 14 (01) ◽  
pp. 107-117
Author(s):  
XIAOLI ZHI ◽  
RONG LU ◽  
XINDA LU
Keyword(s):  
Dirichlet Boundary ◽  
Three Dimensional ◽  
Software Tool ◽  
Dirichlet Boundary Conditions ◽  
Diffusion Equations ◽  
Fractional Step ◽  
Unconditionally Stable ◽  
Convection Diffusion ◽  
Parallel Solver ◽  
Iteration Technique

A parallel unconditionally stable solver for three-dimensional convection-diffusion equations is proposed by applying the upwind Crank-Nicolson difference schemes combined with alternating bar parallelization. This solver can be applied numerically to any variation of convection-diffusion equations with Dirichlet boundary conditions. Making use of a fractional step iteration technique for linear systems, this approach yields good runtime performance. To validate the accuracy and efficiency of the method, sample experiments are done on a software tool, Codie4D, which was implemented using the MPICH library.

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