3차원 비선형 자유표면유동의 수치해석을 위한 3차경계요소법의 정확도와 수렴성 고찰

Abstract

The present paper deals with the accuracy and convergence of the third-order boundary element method(BEM), which was originally developed by Grilli et al.(2000). There has been no sincere consideration on practical questions on such as the required number of node points for nonlinear water wave simulation with this BEM. We suggest a simple answer for this matter by taking a close look at the resulting errors for the linear wave potential function in a rectangular domain with flat and wavy top surface. According to the test computation, we revealed that the convergence rate is of the third-order, and that we are able to get the numerical error less than 1% for highly nonlinear waves by using 8 elements per a wavelength at least with the present third-order element. At the same time, we indicated that the dependency of CPU time upon the number of unknowns for the present BEM with the fast multipole algorithm(FMA). Conclusively, we have shown that the present BEM is accurate and convergent for three dimensional nonlinear water waves for the context of the mixed Dirichlet-Neumann problem.