Partial semi-coarsening multigrid method based on the HOC scheme on nonuniform grids for the convection–diffusion problems

ABSTRACT

A partial semi-coarsening multigrid method based on the high-order compact (HOC) difference scheme on nonuniform grids is developed to solve the 2D convection–diffusion problems with boundary or internal layers. The significance of this study is that the multigrid method allows different number of grid points along different coordinate directions on nonuniform grids. Numerical experiments on some convection–diffusion problems with boundary or internal layers are conducted. They demonstrate that the partial semi-coarsening multigrid method combined with the HOC scheme on nonuniform grids, without losing the high-order accuracy, is very efficient and effective to decrease the computational cost by reducing the number of grid points along the direction which does not contain boundary or internal layers.

KEYWORDS:

• Convection–diffusion equation
• high-order compact difference scheme
• nonuniform grids
• partial semi-coarsening
• multigrid method
• boundary or internal layer

2010 AMS SUBJECT CLASSIFICATIONS:

• 65M06
• 65M12

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The present work was supported by the National Natural Science Foundation of China [grant number 11061025], [grant number 11361045].