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A Cartesian cut cell free surface capturing method for 3D water impact problems

Authors

  • Z. Z. Hu,

    Corresponding author
    • Centre for Mathematical Modelling and Flow Analysis, School of Computing, Mathematics and Digital Technology, The Manchester Metropolitan University, Manchester, M1 5GD, UK
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  • D. M. Causon,

    1. Centre for Mathematical Modelling and Flow Analysis, School of Computing, Mathematics and Digital Technology, The Manchester Metropolitan University, Manchester, M1 5GD, UK
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  • C. G. Mingham,

    1. Centre for Mathematical Modelling and Flow Analysis, School of Computing, Mathematics and Digital Technology, The Manchester Metropolitan University, Manchester, M1 5GD, UK
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  • L. Qian

    1. Centre for Mathematical Modelling and Flow Analysis, School of Computing, Mathematics and Digital Technology, The Manchester Metropolitan University, Manchester, M1 5GD, UK
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Correspondence to: Z. Z. Hu, Centre for Mathematical Modelling and Flow Analysis, School of Computing, Mathematics and Digital Technology, The Manchester Metropolitan University, Manchester, M1 5GD, UK.

E-mail: z.hu@mmu.ac.uk

SUMMARY

A Cartesian cut cell mesh generation procedure is developed together with a finite volume Euler solver for a two-fluid system with a free surface. A fast and robust triangle to triangle overlap scheme is used to determine the intersection of a body-surface with the background Cartesian mesh. Improvements to the cut cell routines include a new treatment for multiple cuts within a single cell and a surface trimming procedure to ensure a good quality mesh around solid boundaries. The formulae for calculating all necessary information about a cut cell are also presented. These are generic and can be used for arbitrarily irregular boundary elements. A collocated finite volume method with a high resolution Godunov-type scheme in space is used for discretization of the governing flow equations. By computing in both the air and water regions simultaneously in a consistent manner, the free surface is automatically captured as a contact discontinuity in the density field without the need for any special free surface tracking method. The algorithm incorporates the artificial compressibility method with a dual time stepping strategy to maintain a divergence free velocity field. The mathematical formulation including its numerical implementation of the method is reviewed and results for a number of test cases are also presented. Copyright © 2012 John Wiley & Sons, Ltd.

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