An Efficient Three-Dimensional FNPF Numerical Wave Tank for Large-Scale Wave Basin Experiment Simulation

Abstract

This paper presents a parallel implementation and validation of an accurate and efficient three-dimensional computational model (3D numerical wave tank), based on fully nonlinear potential flow (FNPF) theory, and its extension to incorporate the motion of a laboratory snake piston wavemaker, as well as an absorbing beach, to simulate experiments in a large-scale 3D wave basin. This work is part of a long-term effort to develop a “virtual ” computational wave basin to facilitate and complement large-scale physical wave-basin experiments. The code is based on a higher-order boundary-element method combined with a fast multipole algorithm (FMA). Particular efforts were devoted to making the code efficient for large-scale simulations using high-performance computing platforms. The numerical simulation capability can be tailored to serve as an optimization tool at the planning and detailed design stages of large-scale experiments at a specific basin by duplicating its exact physical and algorithmic features. To date, waves that can be generated in the numerical wave tank (NWT) include solitary, cnoidal, and airy waves. In this paper we detail the wave-basin model, mathematical formulation, wave generation, and analyze the performance of the parallelized FNPF-BEM-FMA code as a function of numerical parameters. Experimental or analytical comparisons with NWT results are provided for several cases to assess the accuracy and applicability of the numerical model to practical engineering problems. [DOI: 10.1115/1.4007597

A nonoverlapping heterogeneous domain decomposition method for three-dimensional gravity wave impact problems

“…Here τ and ξ denote proper time and space scale, respectively. The long waves described by the KdV equation (13) have the exact counteracting dispersiveness and nonlinearity effects, therefore can maintain their profiles for a long duration. In Eq.…”

“…The wave is generated in Ω PF , and an array consisting of three cylinders is situated downstream. The theory of wave making and its validation of the BEM solver is discussed by Grilli and coworkers in [10,13,44]. The solitary wave has a height of H = 0.6h.…”

“…The PF problem is solved using a BEM proposed by Grilli et al [10,44], Fochesato and Dias [45] and Nimmala et al [13]. The BEM is based on the boundary integral equation (BIE) of the Laplace's equation, see, e.g., [73]).…”

“…The model could be viscous flow, governed by the Navier-Stokes equations (NSE), such as the work by Lin and Liu [5], Park et al [6], Yuan et al [7], and Li et al [8]. It could also be a simplified model such as potential flow (PF) or Boussinesq model, such as the work by Beji and Battjes [9], Grilli et al [10], Ryu et al [11], Liu et al [12] and Nimmala et al [13]. An extensive review of using PF solutions to NWT using the boundary integral equation (BIE) approach is given by Kim et al [14].…”

“…The PF subdomain is solved using a boundary element method (BEM), whereas NSE subdomain is solved using a finite element method (FEM). The BEM solver is based on the work of Grilli et al [10,44], Fochesato and Dias [45], and Nimmala et al [13]. The BIE from the Laplace equation is discretized using a collocation BEM, and the linear system is solved using the generalized minimal residual method (GMRES) accelerated by the fast multipole method (FMM).…”