We derive a new fourth order compact finite difference scheme which allows different meshsize in different coordinate directions for the two-dimensional convection diffusion equation. A multilevel local mesh refinement strategy is used to deal with the local singularity problem. A corresponding multilevel multigrid method is designed to solve the resulting sparse linear system. Numerical experiments are conducted to show that the local mesh refinement strategy works well with the high order compact discretization scheme to recover high order accuracy for the computed solution. Our solution method is also shown to be effective and robust with respect to the level of mesh refinement and the anisotropy of the problems.
|Number of pages||14|
|Journal||Computer Methods in Applied Mechanics and Engineering|
|State||Published - Sep 13 2002|
Bibliographical noteFunding Information:
Jun Zhang’s research work was supported in part by the U.S. National Science Foundation under grants CCR-9902022, CCR-9988165, CCR-0092532, CCR-0117602, in part by the Japan Research Organization for Information Science & Technology, and in part by the University of Kentucky Center for Computational Sciences. Haiwei Sun’s research work was supported by U.S. National Science Foundation under grant CCR-9988165. Jennifer J. Zhao’s research work was supported by the U.S. National Science Foundation under grant CCR-0117602.
- Convection diffusion equation
- Local mesh refinement
- Multigrid method
- Singularity and boundary layer
ASJC Scopus subject areas
- Computational Mechanics
- Mechanics of Materials
- Mechanical Engineering
- Physics and Astronomy (all)
- Computer Science Applications