Abstract
This paper describes a parallel convection-diffusion solver which may be used as part of a Navier-Stokes solver for three-dimensional channel flow at moderately large Reynolds numbers [S. Turek, Efficient Solvers for Incompessible Flow Problems: An Algorithmic Approach in View of Computational Aspects, Springer-Verlag, 1999]. The solver uses a multiplicative Schwarz domain decomposition with overlapping subdomains to solve singularly perturbed convection-diffusion equations where convection is dominant. Upwind finite differences are used for the spatial discretization. The algorithm uses special features of the singularly perturbed convection-diffusion operator. The error due to a local perturbation of the boundary conditions decays extremely fast, in the upwind as well as the crosswind direction, so the overlap in the domain decomposition can be kept to a minimum. The algorithm parallelizes well and is particularly suited for applications in three dimensions. Results of two- and three-dimensional numerical experiments are presented.
Original language | English (US) |
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Pages (from-to) | 891-916 |
Number of pages | 26 |
Journal | SIAM Journal on Scientific Computing |
Volume | 22 |
Issue number | 3 |
DOIs | |
State | Published - 2001 |
Keywords
- Convection-diffusion
- Damping factor
- Maximum principle
- Overlapping domain decomposition
- Upwind finite differences
ASJC Scopus subject areas
- Computational Mathematics
- Applied Mathematics