## Abstract

An unstructured overset method capable of performing direct numerical simulation (DNS) and large eddy simulation (LES) of many (O(10^{5})) moving bodies, utilizing many computational cores (O(10^{5})), in turbulent, incompressible fluid flow is presented. Unstructured meshes are attached to bodies and placed within a fixed background domain. Body meshes are allowed to arbitrarily overlap and move throughout the domain. Within each mesh a high resolution, unstructured, non-dissipative finite volume method is used to solve for the flow field. Boundary conditions for each mesh are provided by interpolation from flow solutions on overlapping meshes. When many unstructured meshes of different resolution overlap, care is required in the connection between the different flow solutions. An interpolant is created which seeks to preserve volume conservation of flow quantities between meshes regardless of overlapping mesh differences. An implicit fractional step method is used for time advancement, requiring the calculation of a predicted fluid velocity and corrector pressure field. For the predictor step, the resulting interpolation is directly introduced into the implicit equations for the predicted flow field. For the corrected pressure field, the continuity between meshes is weakly enforced using a penalty formulation. The pressure formulation is symmetric, positive-definite and non-singular resulting in a formulation which is readily solvable using traditional iterative matrix inversion techniques. An Arbitrary Euler-Lagrangian (ALE) method coupled to a 6 degrees of freedom rigid body equation system (6-DOF) is used for body motion. For rotation, a quaternion representation is used to solve Euler's equations of rigid body motion. A linear spring damper model, which uses geometry information readily available from the overset assembly process, is used for collisions. Validation of the method for canonical flow fields is presented including assessment of order of accuracy and kinetic energy conservation properties. Particle-resolved direct numerical simulation (PR-DNS) of single particles in various flow fields are presented for validation. PR-DNS results of 50,000 spherical particles freely moving within turbulent channel flow are shown as a demonstration of the method at full scale. LES results of a marine propeller under crashback conditions are shown to demonstrate the ability to simulate highly unsteady turbulent flows over complex, moving geometries.

Original language | English (US) |
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Article number | 108790 |

Journal | Journal of Computational Physics |

Volume | 397 |

DOIs | |

State | Published - Nov 15 2019 |

### Bibliographical note

Funding Information:The work was made possible by computational resources provided by Department of Energy as part of the Predictive Academic Alliance Program (PSAAP2) through the Department of Energy under DE-NA0002373 . Further resources for this work were provided by the National Science Foundation (NSF) under NSF Grant CBET-1510154 . Sreevatsa Anantharamu is gratefully acknowledged for providing the large channel mesh required for the particle-laden channel result. Praveen Kumar, Thomas Kroll and Karim Alame are acknowledged for creating meshes for use in the crashback simulations and for providing helpful input in using the method to perform LES.

Publisher Copyright:

© 2019 Elsevier Inc.

## Keywords

- Conservative
- DNS
- LES
- Overset
- Parallel
- Unstructured