Journal
SYMMETRY-BASEL
Volume 13, Issue 7, Pages -Publisher
MDPI
DOI: 10.3390/sym13071123
Keywords
3D convection-diffusion equation; HOC scheme; non-uniform grids; multigrid method; partial semi-coarsening
Categories
Funding
- National Natural Science Foundation of China [11772165, 11961054, 11902170, 11801287]
- Inner Mongolia Autonomous Region Youth Science and Technology Talents support program [NJYT20B15]
- Inner Mongolia Scientific Fund Project [2018BS01002, 2018LH01008]
- Innovation Fund Project of Inner Mongolia University of Science and Technology-Excellent Youth Science Fund Project [2019YQL02]
- National Youth Top-Notch Talent Support Program of Ningxia
- First Class Discipline Construction Project in Ningxia Universities: Mathematics
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This paper extends previous research on solving convection-diffusion problems in two dimensions to three dimensions using the partial semi-coarsening multigrid method and high-order compact difference scheme. The main advantage of this method is that the multigrid method on non-uniform grids can be performed with different numbers of grids in different coordinate axes, making it more efficient than using the same number of grids in different coordinate axes.
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).
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