WHOLE TIME-DOMAIN APPROACH TO THE INVERSE NATURAL-CONVECTION PROBLEM

A numerical solution is presented for the inverse natural convection p roblem, based on the optimization approach, without specifying any rep resentation of the unknown boundary condition. In this context the min imization of the error, which is at the heart of the solution algorith m, is achieved using conjugate gradients in infinite-dimensional funct ion space. The gradients of the object functional associated with the error are obtained from a system of adjoint equations. The direct, sen sitivity, and adjoint equation systems are solved numerically, using a implicit, control volume discretization procedure. Results are presen ted for two-dimensional flow in a square cavity heated from the side, with the remaining wads adiabatic, at several Rayleigh numbers, for bo th an unsteady uniform flux and a steady nonuniform flux. It is found that the sensitivity, and thereby the accuracy and stability of the me thod are affected by convection and thus depend on the Rayleigh number as wed as the type of boundary conditions. At the present state of th e art the optimization approach by conjugate gradients in infinite-dim ensional function space was shown to provide satisfactory results for inverse convection at Rayleigh numbers < 10(4) with an imposed heat fl ux of the form q = -sin (pi t) cos (pi y).