A high-order finite difference method with immersed-boundary treatment for fully nonlinear wave-structure interaction

Yan Xu*

*Corresponding author for this work

    Research output: Book/ReportPh.D. thesis

    370 Downloads (Pure)

    Abstract

    In order to predict nonlinear wave loading on maritime structures, a fully nonlinear finite difference based potential flow solver with all boundary conditions addressed by an immersed boundary method has been developed in this thesis. Several linear and nonlinear wave propagation and wave-structure interaction problems have been studied to evaluate the accuracy, efficiency and stability features of the solver. The solver adopts an immersed boundary method to track both the free surface and the body surface within a ground fixed Cartesian background grid, and a combination of standard finite differences and weighted least squares stencils are adopted. The time stepping is conducted via an explicit fourth-order Runge-Kutta method. The forces on the structure are computed by employing the acceleration potential method. Before introducing a structure into the domain, the convergence and stability of this approach is first established for the linear wave propagation problem, using various orders of scheme and different grid discretization strategies. The nonlinear wave problem on a flat bottom is then considered, and the solutions are compared with the highly accurate stream function theory solution. The convergence performance of the numerical solution for this nonlinear wave problem is established. Then linear wave shoaling and nonlinear wave propagation over a submerged bar are also tested. Then two test cases of forced oscillation of a cylinder in an infinite fluid are studied, without involving the free surface, which helps to reveal the advantage of the acceleration potential method in terms of wave load computation. When it comes to the wave-body interaction problem, a wave generation problem using a piston type wave maker is fist tested. Cautious attention is paid to the intersection point between free surface and body surface, and a scheme which meets the accuracy and stability requirements best is picked from several proposals. Finally, a forced heaving cylinder on the free surface test is conducted, and the wave load on the cylinder is computed and analysed. A preconditioned iterative solution strategy is also developed and shown to provide optimal scaling of the solution effort with increasing number of unknowns. Finally, a novel hyper-viscosity filter is introduced for the wave maker problem to provide stability on non-uniform grids.
    Original languageEnglish
    Place of PublicationKgs. Lyngby
    PublisherTechnical University of Denmark
    Number of pages90
    ISBN (Electronic)978-87-7475-665-1
    Publication statusPublished - 2021
    SeriesDCAMM Special Report
    NumberS302
    ISSN0903-1685

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