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Converting a mode-splitting scheme into a semi-implicit scheme for free surface flows

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Abstract
We present the modification of the 3-D hydrostatic free surface flow solver COHERENS. The original solver uses the explicit mode-splitting technique, in which the stepping of the surface gravity waves is decoupled from the stepping of the hydrodynamic 3-D currents. As such, CPU-time is gained by adopting fewer 3-D current solutions than 2-D depth-integrated gravity wave solutions. Since the CFL limit for the 2-D mode is inversly proportional to the root mean square of the depth, the mode-splitting technique becomes less efficient for larger water depths. Treating the terms related to gravity implicitly avoids gravity wave time step restriction and the use of mode splitting, while the stability of the code is still guaranteed. On the other hand, it requires an iterative inversion of a system. We present an iterative version of the semi-implicit algorithm. A comparison of the results reveals the equivalence of both algorithms in terms of accuracy. Due to coding inefficiency, the expected gain in CPU-time is not yet obtained for the test case presented. However, with the modifications presented, the robustness of the COHERENS model is increased, allowing larger time steps for complex model applications.
Keywords
hydrostatic, mode-splitting, free-surface, flow solver, Coherens

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Chicago
Rauwoens, Pieter, Tomas Van Oyen, Jan Vierendeels, Peter Troch, Patrick Luyten, A Breugem, and M Heredia Gomez. 2011. “Converting a Mode-splitting Scheme into a Semi-implicit Scheme for Free Surface Flows.” In Fifth International Conference on Advanced Computational Methods in Engineering (ACOMEN 2011), ed. Michel Hogge, Roger Van Keer, Erik Dick , Benny Malengier, Marian Slodicka, Eric Béchet, Christophe Geuzaine, Ludovic Noels, and Jean-François Remacle, 1–9. Liège, Belgium: Université de Liège.
APA
Rauwoens, Pieter, Van Oyen, T., Vierendeels, J., Troch, P., Luyten, P., Breugem, A., & Gomez, M. H. (2011). Converting a mode-splitting scheme into a semi-implicit scheme for free surface flows. In Michel Hogge, R. Van Keer, E. Dick , B. Malengier, M. Slodicka, E. Béchet, C. Geuzaine, et al. (Eds.), Fifth international conference on advanced computational methods in engineering (ACOMEN 2011) (pp. 1–9). Presented at the 5th International conference on Advanced COmputational Methods in ENgineering (ACOMEN 2011), Liège, Belgium: Université de Liège.
Vancouver
1.
Rauwoens P, Van Oyen T, Vierendeels J, Troch P, Luyten P, Breugem A, et al. Converting a mode-splitting scheme into a semi-implicit scheme for free surface flows. In: Hogge M, Van Keer R, Dick E, Malengier B, Slodicka M, Béchet E, et al., editors. Fifth international conference on advanced computational methods in engineering (ACOMEN 2011). Liège, Belgium: Université de Liège; 2011. p. 1–9.
MLA
Rauwoens, Pieter, Tomas Van Oyen, Jan Vierendeels, et al. “Converting a Mode-splitting Scheme into a Semi-implicit Scheme for Free Surface Flows.” Fifth International Conference on Advanced Computational Methods in Engineering (ACOMEN 2011). Ed. Michel Hogge et al. Liège, Belgium: Université de Liège, 2011. 1–9. Print.
@inproceedings{2073973,
  abstract     = {We present the modification of the 3-D hydrostatic free surface flow solver COHERENS. The original solver uses the explicit mode-splitting technique, in which the stepping of the surface gravity waves is decoupled from the stepping of the hydrodynamic 3-D currents. As such, CPU-time is gained by adopting fewer 3-D current solutions than 2-D depth-integrated gravity wave solutions. Since the CFL limit for the 2-D mode is inversly proportional to the root mean square of the depth, the mode-splitting technique becomes less efficient for larger water depths. Treating the terms related to gravity implicitly avoids gravity wave time step restriction and the use of mode splitting, while the stability of the code is still guaranteed. On the other hand, it requires an iterative inversion of a system. We present an iterative version of the semi-implicit algorithm. A comparison of the results reveals the equivalence of both algorithms in terms of accuracy. Due to coding inefficiency, the expected gain in CPU-time is not yet obtained for the test case presented. However, with the modifications presented, the robustness of the COHERENS model is increased, allowing larger time steps for complex model applications.},
  author       = {Rauwoens, Pieter and Van Oyen, Tomas and Vierendeels, Jan and Troch, Peter and Luyten, Patrick and Breugem, A and Gomez, M Heredia},
  booktitle    = {Fifth international conference on advanced computational methods in engineering (ACOMEN 2011)},
  editor       = {Hogge, Michel  and Van Keer, Roger  and Dick , Erik  and Malengier, Benny  and Slodicka, Marian  and B{\'e}chet, Eric  and Geuzaine, Christophe  and Noels, Ludovic  and Remacle, Jean-Fran\c{c}ois },
  isbn         = {9782960114317},
  keyword      = {hydrostatic,mode-splitting,free-surface,flow solver,Coherens},
  language     = {eng},
  location     = {Liege, Belgium},
  pages        = {1--9},
  publisher    = {Universit{\'e} de Li{\`e}ge},
  title        = {Converting a mode-splitting scheme into a semi-implicit scheme for free surface flows},
  year         = {2011},
}