An Eulerian-Lagrangian single-node collocation method for transient advection-diffusion equations in multiple space dimensions

2003 ◽  
Vol 20 (2) ◽  
pp. 284-301 ◽  
Author(s):  
Li Wu ◽  
Hong Wang
Keyword(s):  
Collocation Method ◽  
Diffusion Equations ◽  
Single Node ◽  
Advection Diffusion

scholarly journals A collocation method of lines for two‐sided space‐fractional advection‐diffusion equations with variable coefficients

2019 ◽  
Vol 42 (10) ◽  
pp. 3465-3480 ◽  
Author(s):  
Mohammed K. Almoaeet ◽  
Mostafa Shamsi ◽  
Hassan Khosravian‐Arab ◽  
Delfim F. M. Torres
Keyword(s):  
Collocation Method ◽  
Method Of Lines ◽  
Variable Coefficients ◽  
Diffusion Equations ◽  
Advection Diffusion

scholarly journals Cubic B-Spline Collocation Method for One-Dimensional Heat and Advection-Diffusion Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-8 ◽  
Author(s):  
Joan Goh ◽  
Ahmad Abd. Majid ◽  
Ahmad Izani Md. Ismail
Keyword(s):  
Collocation Method ◽  
Numerical Solutions ◽  
Diffusion Equations ◽  
Test Problems ◽  
Spline Collocation ◽  
Von Neumann ◽  
One Dimensional ◽  
Advection Diffusion ◽  
The Stability ◽  
Good Agreement

Numerical solutions of one-dimensional heat and advection-diffusion equations are obtained by collocation method based on cubicB-spline. Usual finite difference scheme is used for time and space integrations. CubicB-spline is applied as interpolation function. The stability analysis of the scheme is examined by the Von Neumann approach. The efficiency of the method is illustrated by some test problems. The numerical results are found to be in good agreement with the exact solution.

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.

Lie group solutions of advection-diffusion equations

2021 ◽  
Vol 33 (4) ◽  
pp. 046604
Author(s):  
Yubiao Sun ◽  
Amitesh Jayaraman ◽  
Gregory S. Chirikjian
Keyword(s):  
Lie Group ◽  
Diffusion Equations ◽  
Advection Diffusion
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