SHAPE OPTIMIZATION OF THE MAXIMIZING PROBLEM OF THE DISSIPATION ENERGY AND ITS EFFECT ON HYDRODYNAMIC STABILITY

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This paper presents a numerical result for generalized eigenvalue problems on the optimum shape using the numerical method for a flow-field shape optimization problem. The main shape optimization problem addressed in this paper is defined as a two-dimensional lid-driven cavity flow. As an objective cost function, we use the dissipation energy. The domain volume is used as a constraint cost function. The shape derivative of the objective cost function with respect to the domain variation is evaluated using the solution of the main problem and the adjoint problem. Numerical schemes used to conduct the shape optimization problem using an iterative algorithm based on the traction method for reshaping are presented, where the shape of the boundaries aside the top boundary is optimized. Furthermore, by operating a generalized eigenvalue problem, linear neutral curves between the initial domain Ω0 and the optimum shape domain Ω1 are compared. Numerical results reveal that the shape is optimized by satisfying the volume constraint. Based on generalized eigenvalue problems, the critical Reynolds number of the optimum shape Ω1 is larger than that of the initial shape Ω0.