Journal
JOURNAL OF COMPUTATIONAL PHYSICS
Volume 230, Issue 2, Pages 402-424Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2010.09.029
Keywords
High-order boundary element method; Pre-corrected fast Fourier transform; Nonlinear wave dynamics; Nonlinear wave-body interaction; Ship hydrodynamics
Funding
- Office of Naval Research
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A highly efficient high-order boundary element method is developed for the numerical simulation of nonlinear wave-wave and wave-body interactions in the context of potential flow. The method is based on the framework of the quadratic boundary element method (QBEM) for the boundary integral equation and uses the pre-corrected fast Fourier transform (PFFT) algorithm to accelerate the evaluation of far-field influences of source and/or normal dipole distributions on boundary elements. The resulting PFFT-QBEM reduces the computational effort of solving the associated boundary-value problem from O(N-2 similar to 3) (with the traditional QBEM) to O(N ln N) where N represents the total number of boundary unknowns. Significantly, it allows for reliable computations of nonlinear hydrodynamics useful in ship design and marine applications, which are forbidden with the traditional methods on the presently available computing platforms. The formulation and numerical issues in the development and implementation of the PFFT-QBEM are described in detail. The characteristics of accuracy and efficiency of the PFFT-QBEM for various boundary-value problems are studied and compared to those of the existing accelerated (lower-and higher-order) boundary element methods. To illustrate the usefulness of the PFFT-QBEM, it is applied to solve the initial boundary-value problem in the generation of three-dimensional nonlinear waves by a moving ship hull. The predicted wave profile and resistance on the ship are compared to available experimental measurements with satisfactory agreements. (c) 2010 Elsevier Inc. All rights reserved.
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