Parallelization of Implicit Finite Difference Schemes in Computational Fluid Dynamics
Abstract
Implicit finite differences schemes are often the preferred numerical schemes in computational fluid dynamics, requiring less stringent stability bounds than the explicit schemes. Each iteration in an implicit scheme, however, involves global data dependencies in the form of second and higher order recurrences. Efficient parallel implementations of such iterative methods, therefore, are considerably more difficult and non-intuitive. In this paper, we consider the parallelization of the implicit schemes that are used for solving the Euler and the thin layer Navier-Stokes equations and that require inversions of large linear systems in the form of block tri-diagonal and/or block penta- diagonal matrices. We focus our attention on three-dimensional cases an present schemes that minimize the total execution time. We describe partitioning and scheduling schemes for alleviating the effects of the global data dependencies. An analysis of the communication and the computation aspects of these methods is presented. The effect of the boundary conditions on the parallel schemes is also discussed. The ARC-3D code, developed at NASA Ames, is used as an example application. Performance of the proposed methods is verified on the Victor multiprocessor system which is a message passing architecture developed at the IBM, T.J. Watson Research Center. (KR)
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 01, 1990
- Accession Number
- ADA227105
Entities
People
- Michel Nicoules
- Naomi H. Decker
- Vijay K. Naik