Seakeeping with the semi-Lagrangian particle finite element method

Abstract

The application of the semi-Lagrangian particle finite element method (SL–PFEM) for the seakeeping simulation of the wave adaptive modular vehicle under spray generating conditions is presented. The time integration of the Lagrangian advection is done using the explicit integration of the velocity and acceleration along the streamlines (X-IVAS). Despite the suitability of the SL–PFEM for the considered seakeeping application, small time steps were needed in the X-IVAS scheme to control the solution accuracy. A preliminary proposal to overcome this limitation of the X-IVAS scheme for seakeeping simulations is presented.

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Notes

  1. 1.

    The SL–PFEM method using the X-IVAS scheme has been called the particle finite element method second generation (PFEM-2) by the original authors [16]. However, we choose the former nomenclature (SL–PFEM + X-IVAS) to acknowledge its connection (see Sect. 2) with semi-Lagrangian schemes.

  2. 2.

    In multi-fluid flows, the interface between multiple fluids is reconstructed [1] on the FE mesh using the advected particle identities. Appropriate enrichments are determined [1] for the pressure FE shape functions about the interface.

  3. 3.

    http://cordis.europa.eu/project/rcn/200435_en.html

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Acknowledgments

Permission to use the image shown in Fig. 1 has been granted by Prof. Mehdi Ahmadian, VirginiaTech, USA. This image has appeared earlier in Andrew William Peterson’s Ph.D. thesis [25, Fig. 3.12, p. 55].

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Correspondence to Prashanth Nadukandi.

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The authors declare that they have no conflict of interest.

Funding

This study was partially supported by the WAM-V project funded under the Navy Grant N62909-12-1-7101 issued by Office of Naval Research Global, the SAFECON project (ref. 267521, FP7-IDEAS-ERC) and the FORECAST project (ref. 664910, H2020-ERC-2014-PoC) of the European Research Council (European Commission). The United States Government has a royalty-free license throughout the world in all copyrightable material contained herein.

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Nadukandi, P., Servan-Camas, B., Becker, P.A. et al. Seakeeping with the semi-Lagrangian particle finite element method. Comp. Part. Mech. 4, 321–329 (2017). https://doi.org/10.1007/s40571-016-0127-2

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Keywords

  • Particle finite element method
  • Semi-Lagrangian formulations
  • Seakeeping