Parallel-multigrid computation of unsteady incompressible viscous flows using a matrix-free implicit method and high-resolution characteristics-based scheme

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 sc...

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Bibliographic Details
Published in:Computer methods in applied mechanics and engineering Vol. 194; no. 36; pp. 3949 - 3983
Main Authors: Tai, C.H., Zhao, Y., Liew, K.M.
Format: Journal Article
Language:English
Published: Amsterdam Elsevier B.V 01.09.2005
Elsevier
Subjects:
Exact sciences and technology
Fluid dynamics
Fundamental areas of phenomenology (including applications)
General theory
High-order scheme
Matrix-free implicit method
Parallel-multigrid
Physics
Unsteady incompressible viscous flow
Unstructured tetrahedral grid
Unstructured tetrahedral grid
High-order scheme
Unsteady incompressible viscous flow
Matrix-free implicit method
Parallel-multigrid
Compressibility
Parallel algorithms
Cavity flow
Convection
Finite volume methods
Multigrid
Free flow
Method of characteristics
Tetrahedral shape
Step method
Unsteady flow
Experimental study
Incompressible flow
Circular cylinder
Matrix method
Parallel computation
Incompressible fluid
Domain decomposition
Viscous fluids
Shared memory
Parallelization
Viscous flow
Navier-Stokes equations
ISSN:0045-7825, 1879-2138
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Summary: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.
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ISSN:0045-7825
1879-2138
DOI:10.1016/j.cma.2004.09.010