Geodesic
Scalable algorithm for incompressible flow simulation on parallel computer systems
Matematičeskoe modelirovanie, Tome 19 (2007) no. 10, pp. 105-128

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The paper is devoted to application of parallel technologies for modelling of incompressible turbulent flows using fine meshes and high-order numerical schemes. Main effort is focused on efficient solution of the Poisson equation which arises from the mass-conservation equation. The Poisson operator representing physical features of the incompressible flow has an infinite speed of propagation of information in the spatial domain and this leads to serious obstacles for the parallelization. For this reason efficient solution of the Poisson equation on a parallel system is of first priority. A flexible and scalable algorithm represented in this paper can be efficiently used on both supercomputers and low-cost clusters. Algorithm is based on combination of tree methods: Fourier decomposition, Direct Schur method and conjugated gradient method. Parallel performance was demonstrated on both typical low-cost cluster and Marenostrum supercomputer of the Barcelona Supercomputing Center. An application of the algorithm for a large direct numerical simulation on 512 processors is also described. 
@article{MM_2007_19_10_a8,
     author = {A. V. Gorobets},
     title = {Scalable algorithm for incompressible flow simulation on parallel computer systems},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {105--128},
     publisher = {mathdoc},
     volume = {19},
     number = {10},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2007_19_10_a8/}
}
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A. V. Gorobets. Scalable algorithm for incompressible flow simulation on parallel computer systems. Matematičeskoe modelirovanie, Tome 19 (2007) no. 10, pp. 105-128. http://geodesic.mathdoc.fr/item/MM_2007_19_10_a8/