## Abstract

We deal with efficient techniques for numerical simulation of the incompressible fluid flow based on the Navier–Stokes equations discretized using the isogeometric analysis approach. Typically, the most time-consuming part of the simulation is solving the large saddle-point type linear systems arising from the discretization. These systems can be efficiently solved by Krylov subspace methods, but the choice of the preconditioner is crucial.

In our study we test several preconditioners developed for the incompressible Navier–Stokes equations discretized by a finite element method, which can be found in the literature. We study their efficiency for the linear systems arising from the IgA discretization, where the matrix is usually less sparse compared to those from finite elements.

Our aim is to develop a fast solver for a specific problem of flow in a water turbine. It brings several complications like periodic boundary conditions at nonparallel boundaries and computation in a rotating frame of reference. This makes the system matrix even less sparse with a more complicated sparsity pattern.

In our study we test several preconditioners developed for the incompressible Navier–Stokes equations discretized by a finite element method, which can be found in the literature. We study their efficiency for the linear systems arising from the IgA discretization, where the matrix is usually less sparse compared to those from finite elements.

Our aim is to develop a fast solver for a specific problem of flow in a water turbine. It brings several complications like periodic boundary conditions at nonparallel boundaries and computation in a rotating frame of reference. This makes the system matrix even less sparse with a more complicated sparsity pattern.

Original language | English |
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Title of host publication | Isogeometric Analysis and Applications 2018 |

Editors | H. van Brummelen, C. Vuik, M. Möller, C. Verhoosel, B. Simeon |

Place of Publication | Cham |

Publisher | Springer |

Pages | 77-97 |

Number of pages | 21 |

ISBN (Electronic) | 978-3-030-49836-8 |

ISBN (Print) | 978-3-030-49835-1 |

DOIs | |

Publication status | Published - 2021 |

Event | IGAA: Conference on Isogeometric Analysis and Applications: IGAA 2018 - TU Delft, Delft, Netherlands Duration: 23 Apr 2018 → 26 Apr 2018 Conference number: 3rd |

### Publication series

Name | Lecture Notes in Computational Science and Engineering book series |
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Publisher | Springer |

Volume | 133 |

ISSN (Print) | 1439-7358 |

ISSN (Electronic) | 2197-7100 |

### Conference

Conference | IGAA: Conference on Isogeometric Analysis and Applications |
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Country | Netherlands |

City | Delft |

Period | 23/04/18 → 26/04/18 |