Optimal nozzle design using finite element conjugate gradient based software Z. Mrsa, G. Medic Technical Faculty, University ofRijeka, Vukovarska 58, Abstract The finite element incompressible viscous flow solver, with discretization of total derivative, has been originally developed. Optimization with conjugate gradient method, with finite difference approximation of gradient of objective function and specially tailored mesh generator for chosen shape parametrization in the form of Bezier curve segments, has been used for optimal shape design of the nozzle. Almost identical optimal shape was achieved using different polynomial curve basis and different initial parameter values, qualifying the proposed methodology as appropriate for shape optimization in viscous flow problems. 1 Introduction The shape optimization technique is today accepted engineering tool. It is a promising method for the engineer designer because it can supplement his experience and guide him when designing new geometry or trying to improve the efficiency of the existing one. For the simple geometry and simple flow models, such as 2D airfoils or wing profiles, the shape optimization methods are widely used, but they remain quite unused for complex configurations or complex flow models. For 2D domains and potential flow models a good theory exists for a shape optimization, Pironneau [1] and a lot of papers can be found in literature, e.g. Weeber & Hoole [2], Mrsa [3], Bugeda et al. [4], Mrsa & Sopta [5] and Sopta & Mrsa [6]. Approach of using a cheap direct flow solver and very general robust constraint methods is accepted in 3D industrial aerodynamics design, Fol et al [8] A review of recent advances for modeling of aeronautical flows can be found in Dervieux [7], where genetic algorithms have Transactions on Ecology and the Environment vol 12, © 1996 WIT Press, www.witpress.com, ISSN 1743-3541