## Abstract

We present a multi-block finite-difference solver for massively parallel Direct Numerical Simulations (DNS) of incompressible flows. The algorithm combines the versatility of a multi-block solver with the method of eigenfunctions expansions, to speedup the solution of the pressure Poisson equation. This is achieved by employing FFT-based transforms along one homogeneous direction, which effectively reduce the problem complexity at a low cost. These FFT-based expansions are implemented in a framework that unifies all valid combinations of boundary conditions for this type of method. Subsequently, a geometric multigrid solver is employed to solve the reduced Poisson equation in a multi-block geometry. Particular care was taken here, to guarantee the parallel performance of the multigrid solver when solving the reduced linear systems equations. We have validated the overall numerical algorithm and assessed its performance in a massively parallel setting. The results show that 2- to 8-fold reductions in computational cost may be easily achieved when exploiting FFT-accelerated for the solution of the Poisson equation. The solver, SNaC, has been made freely available and open-source under the terms of an MIT license.

Original language | English |
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Article number | 108194 |

Journal | Computer Physics Communications |

Volume | 271 |

DOIs | |

Publication status | Published - Feb 2022 |

### Bibliographical note

Funding Information:I would like to thank Luca Brandt for interesting discussions, and the first users of SNaC from KTH Mechanics, Arash Banaei, Nazario Mastroianni, and Nicolò Scapin for the invaluable feedback and testing. Dr. Rob Falgout from Lawrence Livermore National Laboratory is thanked for suggesting the “sliced pencils” approach using hypre in Algorithm 2, as an alternative to Algorithm 3. Prof. Fernando Pinho from University of Porto (FEUP) is thanked for kindly providing the validation data from Ref. [43]. Finally, the two anonymous reviewers are thanked for the useful feedback on an earlier version of this manuscript. The computing time for the scaling tests was provided by the Swedish National Infrastructure for Computing (SNIC), and the National Infrastructure for High-Performance Computing and Data Storage in Norway, (Sigma2). This work was supported by the University of Iceland Recruitment Fund grant No. 1515-151341, TURBBLY.

Funding Information:

I would like to thank Luca Brandt for interesting discussions, and the first users of SNaC from KTH Mechanics, Arash Banaei, Nazario Mastroianni, and Nicolò Scapin for the invaluable feedback and testing. Dr. Rob Falgout from Lawrence Livermore National Laboratory is thanked for suggesting the “sliced pencils” approach using hypre in Algorithm 2 , as an alternative to Algorithm 3 . Prof. Fernando Pinho from University of Porto (FEUP) is thanked for kindly providing the validation data from Ref. [43] . Finally, the two anonymous reviewers are thanked for the useful feedback on an earlier version of this manuscript. The computing time for the scaling tests was provided by the Swedish National Infrastructure for Computing (SNIC), and the National Infrastructure for High-Performance Computing and Data Storage in Norway, (Sigma2). This work was supported by the University of Iceland Recruitment Fund grant No. 1515-151341 , TURBBLY.

Publisher Copyright:

© 2021 Elsevier B.V.

## Other keywords

- Computational fluid dynamics
- Direct numerical simulation
- Fast Poisson solver
- High-performance computing
- Multi-block solver