Finite difference solutions for nonlinear water waves using an immersed boundary method

Yan Xu*, Harry B. Bingham, Yanlin Shao

*Corresponding author for this work

Research output: Contribution to conferencePaperResearchpeer-review

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Abstract

This work is motivated by two observations related to numerical solutions for nonlinear wave-structure interaction. First, the combination of an Immersed Boundary Method (IBM) for the body-boundary and a σ transform for the free-surface and bottom boundary, as adopted by [1], requires the construction of an artificial C2 continuous free-surface inside the body. While this can be done with some success in 2D, it is likely to be much more problematic in 3D. Secondly, the work of [2] shows quite promising results for the application of an IBM technique for all domain boundaries in the context of the Harmonic Polynomial Cell (HPC) method. Thus, the goal of the present work is to investigate the accuracy and efficiency of a finite difference method solution where all of the fluid domain boundaries are introduced using the IBM. We establish the accuracy and convergence of the method for nonlinear wave propagation on both constant- and variable-depth fluids, demonstrating that the accuracy is comparable to that achieved by the σ transform approach. A preconditioned GMRES iterative solution strategy is also developed and shown to give optimal scaling of the solution effort in 2D.
Original languageEnglish
Publication date2020
Number of pages4
Publication statusPublished - 2020
Event35th International Workshop on Water Waves and Floating Bodies (IWWWFB 2020) - Seoul National University, Soul, Korea, Republic of
Duration: 26 Apr 202029 Apr 2020

Conference

Conference35th International Workshop on Water Waves and Floating Bodies (IWWWFB 2020)
LocationSeoul National University
Country/TerritoryKorea, Republic of
CitySoul
Period26/04/202029/04/2020

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