Cavity-Shape Identification with Convective Boundary Conditions Using Non-Boundary-Fitted Meshes

Abstract

This article presents a system identification scheme to determine the geometric shape of a cavity with convective boundary condition in a heat-conducting medium using the measured temperatures on the surface of the object. The proposed algorithm is based on the nonlinear minimization of the squared errors between the measured temperatures and the calculated ones. In this article, a new approach based on non-boundary-fitted meshes and gradient smoothing technique is presented for the solution of the direct problem and shape sensitivity analysis. In this method, the domain boundary can be moved independently from the mesh, and the solution of the variable-domain problems can be found easily. The domain parameterization technique using cubic splines is adopted to manipulate the shape variation of the cavity. The conjugate gradient method is used as the optimization algorithm. Some numerical examples are solved to evaluate the applicability of the proposed method in the solution of inverse-geometry problems. In the examples, the effects of mesh size, measurement errors, cavity-shape, cavity size, and the initial guess are examined.

The Islamic Azad University, Shiraz Branch, is gratefully acknowledged for its partial support of the first author.

Additional information

Notes on contributors

Farhang Daneshmand

Farhang Daneshmand is currently a visiting professor at the Department of Mechanical Engineering, McGill University, Montreal, Québec, Canada.