Parallel direct Poisson solver for discretisations with one Fourier diagonalisable direction

In the context of time-accurate numerical simulation of incompressible flows, a Poisson equation needs to be solved at least once per time-step to project the velocity field onto a divergence-free space. Due to the non-local nature of its solution, this elliptic system is one of the most time consum...

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Vydáno v:Journal of computational physics Ročník 230; číslo 12; s. 4723 - 4741
Hlavní autoři: Borrell, R., Lehmkuhl, O., Trias, F.X., Oliva, A.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Kidlington Elsevier Inc 01.06.2011
Elsevier
Témata:
Algorithms
Computational fluid dynamics
Computational techniques
DNS
Exact sciences and technology
FFT
Fluid flow
Mathematical methods in physics
Mathematical models
Parallel Poisson solver
Physics
Schur complement
Solvers
Turbulence
Turbulent flow
Two dimensional
Unstructured meshes
Unstructured meshes
DNS
Parallel Poisson solver
Schur complement
FFT
Two-dimensional systems
Turbulent flow
Reynolds number
Digital simulation
Poisson equation
Conjugate gradient methods
Velocity fields
Calculation methods
Incompressible flow
Divergences
Algorithms
Problem solving
Circular cylinder
Models
Calculation
Performance
ISSN:0021-9991, 1090-2716
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Popis
Shrnutí:In the context of time-accurate numerical simulation of incompressible flows, a Poisson equation needs to be solved at least once per time-step to project the velocity field onto a divergence-free space. Due to the non-local nature of its solution, this elliptic system is one of the most time consuming and difficult to parallelise parts of the code. In this paper, a parallel direct Poisson solver restricted to problems with one uniform periodic direction is presented. It is a combination of a direct Schur-complement based decomposition (DSD) and a Fourier diagonalisation. The latter decomposes the original system into a set of mutually independent 2D systems which are solved by means of the DSD algorithm. Since no restrictions are imposed in the non-periodic directions, the overall algorithm is well-suited for solving problems discretised on extruded 2D unstructured meshes. The load balancing between parallel processes and the parallelisation strategy are also presented and discussed. The scalability of the solver is successfully tested using up to 8192 CPU cores for meshes with up to 10 9 grid points. Finally, the performance of the DSD algorithm as 2D solver is analysed by direct comparison with two preconditioned conjugate gradient methods. For this purpose, the turbulent flow around a circular cylinder at Reynolds numbers 3900 and 10,000 are used as problem models.
Bibliografie:ObjectType-Article-1
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ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2011.02.042