An Application of the Localized Finite Element Method to Two-dimensional Free Surface Wave Problems

2차원 자유표면파 문제에서의 국소 유한요소법의 응용

The numerical calculation for solving boundary-value problem related to potential flows with a free surface is carried out by application of the localized finite element method. Only forced motion of 2-D body in infinitely deep fluid is considered, although this schemes is equally applicable to any first order time-harmonic problems of similar nature. The infinite domain of the fluid is separated into the inner flow field and the outer flow field with common inter-surface boundary. The finite element method is applied to obtain the solution in the inner flow field and the Green functions are utilized to represent the solution in the outer flow field. At the inter-surface boundary, the continuity of the value of potential and the normal derivative of the potential(i.e. matching condition) is conserved. The present method has better computational efficiency than the previous LFEM and the integral equation method of Frank. This enhanced computational efficiency is presumably due to the fact that the present method gives a symmetric coefficient matrix and requires less computational time in calculating the influence coefficient matrix of Green function than the integral equation method. And the irregular frequency desen't exist because the uniqueness of the solution is assured by the such that the exact free surface condition is satisfied on the boundary of the localized finite element region(i.e. inner region). As an example of the above method, the hydrodynamic forces for the circular cylinder and the rectangular cylinders are calculated. In the computed results, the small number of singularity distribution segments($3{\sim}6$) give good result relative to Ursell's and Vugts'.