# Boundary Method for Shape Design Sensitivity Analysis in Solving Free-Surface Flow Problems

• Choi Joo Ho (School of Aerospace and Mechanical Engineering, Hankuk Aviation University) ;
• Kwak H. G. (Department of Aerospace and Mechanical Engineering, Hankuk Aviation University) ;
• Grandhi R. V. (Department of Mechanical and Materials Engineering, Wright State University)
• Published : 2005.12.01

#### Abstract

An efficient boundary-based optimization technique is applied in the numerical computation of free surface flow problems, by reformulating them into the equivalent optimal shape design problems. While the sensitivity in the boundary method has mainly been calculated using the boundary element method (BEM) as an analysis means, the finite element method (FEM) is used in this study because of its popularity and easy-to-use features. The advantage of boundary method is that the design velocity vectors are needed only on the boundary, not over the whole domain. As such, a determination of the complicated domain design velocity field, which is necessary in the domain method, is eliminated, thereby making the process easy to implement and efficient. Seepage and supercavitating flow problem are chosen to illustrate the accuracy and effectiveness of the proposed method.

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