An Arbitrary Lagrangian-Eulerian Regularized Boundary Integral Method for Nonlinear Free-Surface Flows over Complex Topography and Wave-Structure Interaction

The applications of the arbitrary Lagrangian-Eulerian (ALE) method on the regularized boundary integral method (RBIM) for simulating water wave transformation over complex topography and wave-structure inter-action based on fully nonlinear potential theory are presented. When solving the boundary integral equation (BIE), RBIM computes the singular integrals of the source and doublet functions through the coordinate trans-formation. Any high-order quadrature can be directly applied as collocation nodes hence spatial discretization is avoided. Through the same technique, the numerical near singularities of the source and doublet integrals can be handled. The ALE approach is adopted to avoid distorted nodal distribution, which often results from the free surface of highly nonlinear water waves, and to keep the convenience of the application of free-surface boundary conditions. The ALE-RBIM and the Newmark method are coupled iteratively for computing structural dynamics undergoing hydrodynamic excitations. The numerical method is validated through three examples: the run-up and reflection of a solitary wave; the periodic wave propagation over complex topography; and the roll mo-tion of a hinge-fixed floating structure undergoing wave excitations. Several important wave features are captured. The wave-structure interaction is characterized. The advantages of ALE-RBIM over MEL-BEM are shown. Correlations between numerical results and experimental measurements are presented.