Abstract
The development and validation of a parallel unstructured tetrahedral non-nested multigrid method for simulation of unsteady 3D incompressible viscous flow are described in this paper. The Navier-Stokes solver is based on the artificial compressibility method (ACM) and a higher-order characteristics-based finite-volume scheme on unstructured multigrid. 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). There are two parallelization strategies proposed in this work, the first strategy is a one-level parallelization strategy using geometric domain decomposition technique alone, the second strategy is a two-level parallelization strategy that consists of a hybrid of both geometric domain decomposition and data decomposition techniques. The Message- Passing Interface (MPI) Library is used for communication of data and loop arrays are decomposed using the OpenMP standard. The parallel codes using single grid and multigrid are used to simulate steady and unsteady incompressible viscous flows for a 3D lid-driven cavity flow and flow over a 3D circular cylinder for validation and performance evaluation purposes. The speedups and efficiencies obtained by both the parallel solvers are reasonably good for all test cases.
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References
Lallemand, M., Steve, H. and Dervieux, A. “Unstructured Multigridding by Volume Agglomeration”. Computers and Fluids 21, pp397–433. (1992)
Mavriplis, D. “Three-dimensional Multigrid for the Euler Equations”. AIAA Journal 30, pp1753–1761. (1992)
Peraire, J., Morgan, K. and Peiro, J. “Multigrid Solution of the 3D Compressible Euler Equations on Unstructured Tetrahedral Grids”. International Journal for Numerical Methods in Engineering 36, pp 1029–1044. (1993)
Chorin A., A Numerical Method for Solving Incompressible Viscous Flow Problems, Journal of Computational Physics, 2(1), 12–26. (1967)
Tai C.H., Zhao Y., Parallel Unsteady Incompressible Viscous Flow Simulation Using An Unstructured Multigrid Method, Journal of Computational Physics, 192, pp. 277–311.(2003)
Gropp W., Lusk E., Skjellum A., Using MPI: Portable Parallel Programming with the Message-Passing Interface, The MIT Press, Cambridge, Massachusetts. (1994)
OpenMP home page, OpenMP: Simple, Portable, Scalable SMP Programming. http://www.openmp.org. (1999)
Karypis G., and Kumar V., Metis: A Software Package for Partitioning Unstructured Graphs, Partitioning Meshes, and Computing Fill-Reducing Orderings of Sparse Matrices, Version 4.0, University of Minnesota, Department of Computer Science. (1998)
Jiang B., Lin T. L., Povinelli L. A., Large-scale Computation of Incompressible Viscous Flow by Least-Squares Finite Element Method, Computer Methods in Applied Mechanics and Engineering, 114, 213–231. (1994)
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Tai, C.H., Liew, K.M., Zhao, Y. (2005). Parallel Unsteady 3D MG Incompressible Flow. In: Zhang, W., Tong, W., Chen, Z., Glowinski, R. (eds) Current Trends in High Performance Computing and Its Applications. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-27912-1_59
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DOI: https://doi.org/10.1007/3-540-27912-1_59
Publisher Name: Springer, Berlin, Heidelberg
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