Bruce A Finlayson
CHEM E 575
Comparison of numerical techniques: similarity, perturbation, finite difference, Galerkin, orthogonal collocation methods as applied to nonlinear chemical engineering problems.
The course teaches you how to solve linear problems numerically, and then uses the numerical methods to solve nonlinear problems, which is the way the world usually works. The emphasis is on using existing packages; usually we just write driver programs. A variety of tools will be used, to save you time, including MATLAB, Excel, and FEMLAB (a computational fluid dynamics code, CFD). This means that you can learn how to apply the methods, and practice the application, with less effort on your part than you might imagine. The emphasis is on understanding the techniques used in those packages so that we can understand how to use them, how to interpret errors, and have a clue what to do when the standard packages donít work. In past years students from a variety of departments have taken the course successfully and found it valuable. This year I'm adding several topices that are related to molecular dynamics or to multi-scale phenomena.
Student learning goals
General method of instruction
The first two thirds of the course covers the topics: (1) Solving Nonlinear Algebraic Equations (the basis of all the rest), (2) methods to integrate initial value problems (we'll examine standard methods and then analyze the methods being used for molecular dynamics), (3) ordinary differential equations as boundary value problems, and (4) partial differential equations, which is a combination of (2) and (3). The textbook is "Nonlinear Analysis in Chemical Engineering", by Bruce A. Finlayson, Ravenna Park Publishing (2003) (the same as the McGraw-Hill, 1980 book). This book provides the basics, but the course expands on it to include multiphase phenomenon (which frequently arise in chemical engineering), multi-scale phenomena (we'll use viscoelastic flow with closure approximations vs. kinetic theory as the example), high-end computing (direct numerical simulation of turbulence using Fourier transforms), and various topics in finite elements (level sets and satisfying boundary conditions using Lagrangian multipliers). During the last third of the course, I will be lecturing on special topics (some of these) while you will be working on your project. The project is a problem related to your research or job that you can solve; a report and presentation at the end of the class take the place of a final. This has been a popular aspect of the course in past years, since students can work on something that is of direct interest to them and they have expert help available to formulate the problem and choose appropriate strategies. Sometimes published papers come out of the project (with additional work after the course). I will also guide student design teams to develop a finite element program of their own to solve for two-dimensional heat conduction.
Students are only assumed to have a senior math knowledge.
Class assignments and grading
There will be weekly homework assignments; one hour test; and the presentations on your project will be given at the end of the quarter.
Homework, One Test, Project