Mixing Enhancement via Flow Optimization

We consider the problem of mixing enhancement in a diffusive fluid mixture that consists of diffusive physical quantities and a fluid flow in which the physical quantities are immersed. We use the flow as a control variable and then use the physical quantity variance and the magnitude of the control to define a cost functional. By variational principles, we then derive optimality conditions for an optimal flow that minimizes the cost functional and then enhances the mixing. These optimality conditions are represented by a system of nonlinear partial differential equations. Using an iteration method and the finite element method, the system is solved and the numerical result shows that the numerical optimal flow obtained from solving the system gives the minimum of the cost functional and then enhances the mixing