We propose a method with sixth-order accuracy to solve the three-dimensional (3D) convection diffusion equation. We first use a 15-point fourth-order compact discretization scheme to obtain fourth-order solutions on both fine and coarse grids using the multigrid method. Then an iterative mesh refinement technique combined with Richardson extrapolation is used to approximate the sixth-order accurate solution on the fine grid. Numerical results are presented for a variety of test cases to demonstrate the efficiency and accuracy of the proposed method, compared with the standard fourth-order compact scheme.
|Number of pages||13|
|Journal||International Journal of Computer Mathematics|
|State||Published - Feb 1 2015|
Bibliographical noteFunding Information:
This author’s research work was supported in part by NSF under grant CNS-1157162, and in part by NVIDIA research CUDA Teaching Center.
© 2014, © 2014 Taylor & Francis.
- 15-point stencil
- Reynolds number
- convection diffusion equation
- multigrid method
- sixth-order compact scheme
ASJC Scopus subject areas
- Computer Science Applications
- Computational Theory and Mathematics
- Applied Mathematics