Numerical Simulation And Optimization With PDE Model

With the development of science and computer technology, complex and uncertain nonlinear dynamic problems have increasingly become a bottleneck of research in the various disciplines of advanced science and technology. Dynamic optimization is the very effective methods to solve these problems. Modern industrial production process, especially in chemical process, most of them can be represented with dynamic nonlinear model. Thus study on dynamic nonlinear process model has great significance.In recent years with the resources, energy and environment issues becoming more and more prominent, the safety, economy, and environmental protection and its optimization will be more important in the petrochemical, pharmaceutical and food industry and other areas of production process. Most of these processes can be expressed with Partial Differential Equations and Differential Algebraic Equations model. The research for DAE system model has the quite mature theory method but for PDE system, the solving and optimizing methods are relatively less. In this paper, we study PDE system model in order to find the simulation solution and optimization methods.After the study of simulation and optimization algorithm, some process system unit are taken for examples to verify the correctness and practical of the method.The main research works of this paper are as follows:1. According to the present situation of the research at home and abroad, we summarize the most commonly used method in solving the PDE system and simulation technology. This paper describes detailedly the steps of the finite volume method to solve PDE process system, and then put forward the finite volume method to simulate process of PDE system;2. The Simulated Moving Bed Chromatography (Simulated Moving Bed Chromatography, SMBC) technology is the most important separation technology. This paper describes detailedly the modeling theory of SMBC. And then choose average rate theory to model the process. Using the finite volume method to solve the convection diffusion process in convective diffusion reactor, and to simulate moving bed separation process respectively. In the end, the results are compared with other methods to verify the feasibility and effectiveness of the finite volume method;3. The convection diffusion reactor is chosen as the research example, and the PDE model is discreted using the method combined finite difference and collocation point method. Then, the optimization method for PDE model equation is developed. SQP algorithm is used in the convection diffusion reactor optimization calculation, to obtain the optimum operation parameters. The optimization results verify the PDE model optimization algorithm.In the end, the paper is concluded with a summary and prospect of future researches.