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Improving the Performances of a Novel RANS Model for Breaking Water Waves Using a Subgrid Approach and Non-equidistant Layers

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Abstract

Numerical models used in coastal engineering must be computationally efficient while maintaining accuracy at an engineering level. One major weakness of models based on non-hydrostatic Reynolds Averaged Navier–Stokes (RANS) equations is the solution of the Poisson equation used to evolve pressure values over time, accounting for up to 70% of the computational time. We propose a method that uses a differential grid to reduce the computational costs while maintaining a good accuracy: a “subgrid approach”, in which pressure values are computed on a coarse grid while velocities are solved on a finer grid. In addition, the grid resolution is increased near the surface and bottom boundaries. This approach is applied to Iravani et al. (Coast Eng 159:103717, 2020. https://doi.org/10.1016/j.coastaleng.2020.103717) model, which also implements novel free surface boundary conditions for breaking waves. The results show how the computational effort can be reduced up to 70% while providing more than satisfactory results for properties of interest for the coastal engineering practice, like wave height decay and mean water elevation.

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Data availability

The datasets generated during and analyzed during the current study are available from the corresponding author on reasonable request.

References

  1. Iravani, N., Badiei, P., Brocchini, M.: Novel free surface boundary conditions for spilling breaking waves. Coast. Eng. 159, 103717 (2020). https://doi.org/10.1016/j.coastaleng.2020.103717

    Article  Google Scholar 

  2. Ma, G., Shi, F., Kirby, J.T.: Shock-capturing non-hydrostatic model for fully dispersive surface wave processes. Ocean Model 43–44, 22–35 (2012). https://doi.org/10.1016/j.ocemod.2011.12.002

    Article  Google Scholar 

  3. Shi, J., et al.: Pressure decimation and interpolation (PDI) method for a baroclinic non-hydrostatic model. Ocean Model 96, 265–279 (2015). https://doi.org/10.1016/j.ocemod.2015.09.010

    Article  Google Scholar 

  4. Van Reeuwijk, M.: Efficient simulation of non-hydrostatic free-surface flow (Wave simulation with interpolation of the vertical pressure profile) Thesis May 2002, Delft University of Technology, Faculty of Civil Engineering and Geosciences, Section Fluid Mechanics Regards.

  5. Rijnsdorp, D.P., Smit, P.B., Zijlema, M., Reniers, A.J.H.M.: Efficient non-hydrostatic modelling of 3D wave-induced currents using a subgrid approach. Ocean Model 116, 118–133 (2017). https://doi.org/10.1016/j.ocemod.2017.06.012

    Article  Google Scholar 

  6. Rijnsdorp, D.P., Smit, P.B., Zijlema, M.: Non-hydrostatic modelling of infragravity waves under laboratory conditions. Coast. Eng. 85, 30–42 (2014). https://doi.org/10.1016/j.coastaleng.2013.11.011

    Article  Google Scholar 

  7. Brocchini, M.: Free surface boundary conditions at a bubbly/weakly splashing air–water interface. Phys. Fluids 14(6), 1834–1840 (2002). https://doi.org/10.1063/1.1475998

    Article  MathSciNet  MATH  Google Scholar 

  8. Ting, F.C.K.K., Kirby, J.T.: Observation of undertow and turbulence in a laboratory surf zone. Coast. Eng. 24(1–2), 51–80 (1994). https://doi.org/10.1016/0378-3839(94)90026-4

    Article  Google Scholar 

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Authors and Affiliations

  1. School of Civil Engineering, College of Engineering, University of Tehran, Tehran, Iran

    Nikta Iravani & Peyman Badiei

  2. Università Politecnica Delle Marche, Ancona, Italy

    Maurizio Brocchini

Authors
  1. Nikta Iravani
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  2. Peyman Badiei
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  3. Maurizio Brocchini
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Correspondence to Nikta Iravani.

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Appendix

Appendix

The following figures show the comparison between numerical results and experimental data of Ting and Kirby [8] for the TKE and velocity profiles. As indicated in the captions, different grid configurations and numerical methods are used Figs. 16, 17, 18, 19, 20, 21, 22.

Fig. 16
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Vertical profiles of the averaged TKE and averaged horizontal velocities at different measuring stations with different numbers of non-equidistant layers (two upper layers and two lower layers have a thickness equal to 0.05)

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Vertical profiles of averaged TKE and averaged horizontal velocities at different measuring stations for a 10-layer grid with different numbers of fine layers near the surface and the bottom

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Vertical profiles of averaged horizontal velocity and averaged TKE using different numbers of layers for the coarse grid

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Comparison between the numerical results and the experimental data of the Spilling breaker case of Ting & Kirby for the time-averaged velocities and time-averaged TKE. a Solving the momentum equation on the fine grid (blue dotted line), b solving the vertical momentum equation on the coarse grid (continuous red line)

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Comparison between the numerical results and the experimental data of the Spilling breaker case of Ting & Kirby. Different resolutions have been used for the fine and coarse grid

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Fig. 21
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Comparison between the numerical results and the experimental data of the Spilling breaker case of Ting and Kirby. a Solving the vertical momentum equation on the coarse grid (green dotted line), b solving the vertical momentum equation on the fine grid (continuous red line)

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Fig. 22
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Comparison between the numerical results and the experimental data of the Spilling breaker case of Ting & Kirby. a Linear pressure interpolation (blue dotted line), b Spline interpolation (continuous red line)

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Iravani, N., Badiei, P. & Brocchini, M. Improving the Performances of a Novel RANS Model for Breaking Water Waves Using a Subgrid Approach and Non-equidistant Layers. Water Waves 4, 447–490 (2022). https://doi.org/10.1007/s42286-022-00066-4

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  • DOI: https://doi.org/10.1007/s42286-022-00066-4

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