An approach combining body-fitted grid generation and conjugate gradient methods for shape design in heat conduction problems

The present study is focused on the development of a computational method for shape design of heat conduction problems by using a combination of the body-fitted grid-generation scheme and the conjugate gradient optimization method. The body-fitted coordinate transformation technique is used to generate a curvilinear grid for each iteration automatically, by sensing the change of the shape of the solution domain during the optimization process. The conjugate gradient method is incorporated with direct sensitivity analysis for seeking the optimal shape which minimizes the objective function. The temperature distribution in the solution domain is solved by means of the finite volume method. A practical problem is used for demonstration, and the results show that the proposed method provides a simple and efficient approach for determining the shape profile.