Nonlinear time‐domain wave‐structure interaction: A parallel fast integral equation approach

Abstract

We report on the development and validation of a new Numerical Wave Tank (NWT) solving fully nonlinear potential flow (FNPF) equations, as a more efficient variation of Grilli et al.'s NWT [Grilli et al., A fully nonlinear model for three-dimensional overturning waves over arbitrary bottom, International Journal for Numerical Methods in Fluids 35 ( 2001) 829-867], which was successful at modeling many wave phenomena, including landslide-generated tsunamis, rogue waves, and the initiation of wave breaking over slopes. This earlier NWT combined a three dimensional MII (mid-interval interpolation) boundary element method (BEM) to an explicit mixed Eulerian-Lagrangian time integration. The latter was based on second-order Taylor series expansions for the mesh geometry and Dirichlet free surface boundary condition for the potential, requiring high-order derivatives to be computed in space and time. Here, to be able to solve large scale wave-structure interaction problems for surface-piercing bodies of complex geometry, of interest for ocean engineering and naval hydrodynamics applications, the NWT is reformulated to use cubic Bspline meshes and the BEM solution is accelerated with a parallelized Fast Multipole Method (FMM) based on ExaFMM, one of the fastest open source FMM to date. The NWT accuracy, convergence, and scaling are first assessed for simple cases, by comparing results with those of the earlier MII-NWT as a function of mesh size and other model parameters. The relevance of the new NWT for solving the targeted applications is then demonstrated for surface piercing fixed cylinders, for which we show that results agree well with theoretical and experimental data for wave elevation and hydrodynamic forces.

Hybrid Lattice-Boltzmann-Potential Flow Simulations of Turbulent Flow around Submerged Structures

“…More accurate results would be obtained by solving potential flow equations for the actual NACA-0012 foil geometry using a higher-order Boundary Element Method. This will be reported on elsewhere, see, e.g., [18,20,48]. Figure 8b shows the module of the inviscid u I i (middle), perturbation u P i (bottom), and total flow u i = u P i + u I i (top) components around the foil, in the finest discretization ∆x/C = 2.5 × 10 −3 , for θ = 4 • .…”

“…To this effect, a generic numerical solver, such as that based on the higher-order Boundary Element Method (BEM), have been used that feature fully nonlinear free surface boundary conditions if applicable e.g., [4,19]. For simulating fully nonlinear wave-structure interactions in large three-dimensional (3D) domains, efficient BEM solvers with a parallelized Fast Multipole Algorithm (FMA) have been developed [20]. Cases with a free surface are not considered in the present paper, but have been reported on elsewhere.…”

“…Therefore, Janssen [9] suggested that instead, the nonlinear I − P coupling terms could directly be introduced into the LBM equilibrium probability distribution functions (EPDFs), hence, to develop perturbation EPDFs or pEPDFs. The latter were incrementally developed, implemented, and validated as part of the development of a perturbation LBM (pLBM) model component to a hybrid naval hydrodynamic solver by [18,[24][25][26], in which the potential flow solution, with fully nonlinear free surface boundary conditions (FNPF), was computed using a higher-order BEM-FMA model [20].…”

An efficient p‐multigrid spectral element model for fully nonlinear water waves and fixed bodies

“…Furthermore, the majority of practical simulation scenarios requires adaptive unstructured grids. Other high‐order numerical methods that addresses the wave propagation problem and the wave‐body problem in a single solver strategy is the high‐order boundary element method 17‐19 that is particularly strong in handling the geometry using unstructured grids, but is limited in terms of numerical efficiency due to inefficient asymptotic scaling of work effort as a result of high computational complexity in the discrete solution of the resulting system of equations in the solver. The spectral wave explicit Navier–Stokes equations technique alleviates the efficiency problem of CFD tools through a decomposition approach to handle wave‐structure applications 20,21 .…”