Abstract
The subject of this paper is an out-of-core implementation of Chorin’s projection method for the three-dimensional, time-dependent, incompressible Navier-Stokes equations in a periodic box. The implementation is particularly suitable for an architecture such as that of the Cray X-MP/SSD, in which a moderate-sized central memory is coupled to a much larger sequential-access memory. The central-memory requirements are only proportional to N2, not N3. Asynchronous i/o techniques are used to overlap i/o with computation and also i/o with itself. All inner loops are successfully vectorized by the Cray Fortran compiler. On the Cray X-MP/SSD, in the case N = 64, the implementation achieves a balanced distribution of cost between i/o and computation. At N = 128, the i/o efficiency is further increased, and the effective megaflop rate (megaflops/wall time) on a single processor with a dedicated machine is 77 megaflops/sec.
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To Peter Lax, with thanks for the Lax Report, which has led to expanded availability of supercomputers for scientific research, and with further thanks for letting CSP practice Mathematics without a license.
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© 1987 Springer-Verlag New York Inc.
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Greenberg, S., McQueen, D.M., Peskin, C.S. (1987). Three-Dimensional Fluid Dynamics in a Two-Dimensional Amount of Central Memory. In: Chorin, A.J., Majda, A.J. (eds) Wave Motion: Theory, Modelling, and Computation. Mathematical Sciences Research Institute Publications, vol 7. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-9583-6_5
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DOI: https://doi.org/10.1007/978-1-4613-9583-6_5
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