Shape identification for natural convection problems using the adjoint variable method

An inverse geometry problem is investigated to identify the boundary shape of a domain from temperature measurements on the other boundary, where the temperature field is dominated by natural convection. The potential applications of the present investigation are the determination of a phase change isotherm in the Bridgman crystal growth or the thermal tomography which detects flaws in materials nondestructively. The inverse problem is posed as a minimization problem of the performance function, which is the sum of square residuals between calculated and observed temperature, by means of a conjugate gradient method employing the adjoint variable method. The present method is found to identify the domains reasonably accurately even with noisy temperature measurements.