On the solution of an inverse natural convection problem using various conjugate gradient methods

The inverse problem of determining the time-varying strength of a heat sour ce, which causes natural convection in a two-dimensional cavity, is conside red. The Boussinesq equation is used to model the natural convection induce d by the heat source. The inverse natural convection problem is solved thro ugh the minimization of a performance function utilizing the conjugate grad ient method. The gradient of the performance function needed in the minimiz ation procedure of the conjugate gradient method is obtained by employing e ither the adjoint variable method or the direct differentiation method. The accuracy and efficiency of these two methods are compared, and a new metho d is suggested that exploits the advantageous aspects of both methods while avoiding the shortcomings of: them. Copyright (C) 2000 John Wiley & Sons, Ltd.