Downwind Numbering : A Robust Multigrid Method for Convection-Diffusion Problems on Unstructured Grids

1995 ◽  
pp. 63-73 ◽  
Author(s):  
Jürgen Bey ◽  
Gabriel Wittum
Keyword(s):  
Multigrid Method ◽  
Unstructured Grids ◽  
Convection Diffusion ◽  
Robust Multigrid ◽  
Diffusion Problems

scholarly journals A Special Multigrid Strategy on Non-Uniform Grids for Solving 3D Convection–Diffusion Problems with Boundary/Interior Layers

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1123
Author(s):  
Tianlong Ma ◽  
Lin Zhang ◽  
Fujun Cao ◽  
Yongbin Ge
Keyword(s):  
Present Method ◽  
Multigrid Method ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Finite Difference Schemes ◽  
Interior Layer ◽  
Convection Diffusion ◽  
Uniform Grids ◽  
Interior Layers ◽  
Diffusion Problems

Boundary or interior layer problems of high-dimensional convection–diffusion equations have distinct asymmetry. Consequently, computational grid distributions and linear algebraic systems arising from finite difference schemes for them are also asymmetric. Numerical solutions for these kinds of problems are more complicated than those symmetric problems. In this paper, we extended our previous work on the partial semi-coarsening multigrid method combined with the high-order compact (HOC) difference scheme for solving the two-dimensional (2D) convection–diffusion problems on non-uniform grids to the three-dimensional (3D) cases. The main merit of the present method is that the multigrid method on non-uniform grids can be performed with a different number of grids in different coordinate axes, which is more efficient than the multigrid method on non-uniform grids with the same number of grids in different coordinate axes. Numerical experiments are carried out to validate the accuracy and efficiency of the present method. It is shown that, without losing the high precision, the present method is very effective to reduce computing cost by cutting down the number of grids in the direction(s) which does/do not contain boundary or interior layer(s).

scholarly journals A hybrid multigrid method for convection–diffusion problems

2014 ◽  
Vol 259 ◽  
pp. 711-719 ◽  
Author(s):  
S. Chaabane Khelifi ◽  
N. Méchitoua ◽  
F. Hülsemann ◽  
F. Magoulès
Keyword(s):  
Multigrid Method ◽  
Convection Diffusion ◽  
Diffusion Problems
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