ポテンシャル流れ場の領域最適化解析

概要

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We present a numerical analysis method for optimization problems of domains in which incompressible potential flow problems are defined. Our idea is to apply the traction method that was proposed as a solution to the domain optimization problems in which elliptic boundary value problems are defined. The traction method is implemented to analyze the speed field, which represents the domain variation, with regard to the deformation field of the linear elastic continuum formed in the objective domain applying the force in proportion to the shape gradient function. In the previous paper, we applied the numerical analysis method based on the traction method to the viscous flow problems in which we chose the total dissipation energy for the objective functional. In the case of potential flow problems, we select the velocity square error norm that is defined to a prescribed velocity in an indicated sub region of the design region, as the objective functional. Using the Lagrange multiplier method we obtain the shape gradient function for these problems. For the numerical analyses we employ the finite-element method. The successful results to two-dimensional problems of a straight channel and a nozzle show the validity of the presented method.
一般社団法人日本機械学会の論文
1995-01-25