Optimal Control of Chemical Processes

Chemical reactive flows lead to optimization problems governed by systems of convection diffusion partial differential equations (PDEs) with nonlinear reaction mechanisms. Such problems are strongly coupled as inaccuracies in one unknown directly affect all other unknowns. Prediction of these unknowns is very important for the safe and economical operation of biochemical and chemical engineering processes. The solution of these PDEs can exhibit boundary and/or interior layers on small regions where the solution has large gradients, when convection dominates diffusion. Hence, special numerical techniques are required, which take the structure of the convection into acount. Recently, discontinuous Galerkin (DG) methods became an alternative to the finite difference, finite volume and continuous finite element methods for solving wave dominated problems like convection diffusion equations since they possess higher accuracy. We focus here on an application of adaptive DG methods for (un)steady optimal control problems governed by copuled convection dominated PDEs with nonlinear reaction terms with state and/or control constraints in 2D and 3D.