An algebraic variational multiscale–multigrid method based on plain aggregation for convection–diffusion problems

2009 ◽  
Vol 198 (47-48) ◽  
pp. 3821-3835 ◽  
Author(s):  
Volker Gravemeier ◽  
Michael W. Gee ◽  
Wolfgang A. Wall
Keyword(s):  
Multigrid Method ◽  
Convection Diffusion ◽  
Variational Multiscale ◽  
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).

A Hybrid Variational Multiscale Element-Free Galerkin Method for Convection-Diffusion Problems

2019 ◽  
Vol 11 (07) ◽  
pp. 1950063 ◽  
Author(s):  
Jufeng Wang ◽  
Fengxin Sun
Keyword(s):  
Splitting Method ◽  
Two Dimensional ◽  
One Dimensional ◽  
Convection Diffusion ◽  
Variational Multiscale ◽  
Discrete Equations ◽  
Element Free Galerkin ◽  
Oscillating Solutions ◽  
Element Free ◽  
Diffusion Problems

By coupling the dimension splitting method (DSM) and the variational multiscale element-free Galerkin (VMEFG) method, a hybrid variational multiscale element-free Galerkin (HVMEFG) method is developed for the two-dimensional convection-diffusion problems. In the HVMEFG method, the two-dimensional problem is converted into a battery of one-dimensional problems by the DSM. Combining the non-singular improved interpolating moving least-squares (IIMLS) method, the VMEFG method is used to obtain the discrete equations of the one-dimensional problems on the splitting plane. Then, final discretized equations of the entire convection-diffusion problems are assembled by the IIMLS method. The HVMEFG method has high accuracy and efficiency. Numerical examples show that the HVMEFG method can obtain non-oscillating solutions and has higher efficiency and accuracy than the EFG and VMEFG methods for convection-diffusion problems.

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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