Abstract
A three-dimensional parallel unstructured non-nested multigrid solver for solutions of unsteady incompressible viscous flow is developed and validated. The finite-volume Navier-Stokes solver is based on the artificial compressibility approach with a high-resolution method of characteristics-based scheme for handling convection terms. The unsteady flow is calculated with a matrix-free implicit dual time stepping scheme. The parallelization of the multigrid solver is achieved by multigrid domain decomposition approach (MG-DD), using single program multiple data (SPMD) and multiple instruction multiple data (MIMD) programming paradigm. There are two parallelization strategies proposed in this work, first strategy is a one-level parallelization strategy using geometric domain decomposition technique alone, second strategy is a two-level parallelization strategy that consists of a hybrid of both geometric domain decomposition and data decomposition techniques. Message-passing interface (MPI) and OpenMP standard are used to communicate data between processors and decompose loop iterations arrays, respectively. The parallel-multigrid code is used to simulate both steady and unsteady incompressible viscous flows over a circular cylinder and a lid-driven cavity flow. A maximum speedup of 22.5 could be achieved on 32 processors, for instance, the lid-driven cavity flow of Re = 1000. The results obtained agree well with numerical solutions obtained by other researchers as well as experimental measurements. A detailed study of the time step size and number of pseudo-sub-iterations per time step required for simulating unsteady flow are presented in this paper.
Original language | English |
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Pages (from-to) | 3949-3983 |
Number of pages | 35 |
Journal | Computer Methods in Applied Mechanics and Engineering |
Volume | 194 |
Issue number | 36-38 |
DOIs | |
Publication status | Published - Sept 23 2005 |
Externally published | Yes |
Funding
This research work was supported by a research scholarship provided by Nanyang Technological University (NTU) and Sun Microsystems Pte. Ltd. The provision of computing facilities by Nanyang Centre for Supercomputing and Visualisation (NCSV), NTU is acknowledged.
Keywords
- High-order scheme
- Matrix-free implicit method
- Parallel-multigrid
- Unsteady incompressible viscous flow
- Unstructured tetrahedral grid
ASJC Scopus subject areas
- Mechanics of Materials
- Mechanical Engineering
- General Physics and Astronomy
- Computer Science Applications
- Computational Mechanics