Designing the Optimal Shape of a Nozzle by the Method of Fundamental Solutions

Abstract

In this paper, we propose a numerical technique based on the method of fundamental solutions (MFS) for solving a classical optimal shape design problem. The problem contains a free boundary condition which should be approximated to find the optimal domain for the solution of Laplace equation. For solving the considered optimization problem, we introduce a meshless regularization technique based on the combination of the MFS and application of the Tikhonov’s regularization method and reduce the problem to solve a system of nonlinear equations. A brief sensitivity analysis on model parameters including the position and the size of the subregion D as well the error with boundary conditions is discussed. Numerical simulations while solving several test examples are presented to show the applicability of the proposed method in obtaining satisfactory results.