MATLAB® has become one of the prominent languages used in research and industry and often described as "the language of technical computing". The focus of this book will be to highlight the use of MATLAB® in technical computing; or more specifically, in solving problems in Process Simulations. This book aims to bring a practical approach to expounding theories: both numerical aspects of stability and convergence, as well as linear and nonlinear analysis of systems.
The book is divided into three parts which are laid out with a "Process Analysis" viewpoint. First part covers system dynamics followed by solution of linear and nonlinear equations, including Differential Algebraic Equations (DAE) while the last part covers function approximation and optimization. Intended to be an advanced level textbook for numerical methods, simulation and analysis of process systems and computational programming lab, it covers following key points
• Comprehensive coverage of numerical analyses based on MATLAB for chemical process examples.
• Includes analysis of transient behavior of chemical processes.
• Discusses coding hygiene, process animation and GUI exclusively.
• Treatment of process dynamics, linear stability, nonlinear analysis and function approximation through contemporary examples.
• Focus on simulation using MATLAB to solve ODEs and PDEs that are frequently encountered in process systems.
Table of Contents
CHAPTER 1 INTRODUCTION
1.1. A GENERAL MODEL
1.2. STRUCTURE OF A MATLAB CODE
1.3. APPROXIMATIONS AND ERRORS IN NUMERICAL METHODS
1.4. ERROR ANALYSIS
1.5. PROCESS EXAMPLES: A PRELUDE
CHAPTER 2 LINEAR ALGEBRA
2.2. VECTOR SPACES
2.3. SINGULAR VALUE DECOMPOSITION
2.4. EIGENVALUES AND EIGENVECTORS
CHAPTER 3 ORDINARY DIFFERENTIAL EQUATIONS: EXPLICIT METHODS
3.1. GENERAL SETUP
3.2. SECOND ORDER METHODS – A JOURNEY THROUGH THE WOODS
3.3. HIGHER-ORDER RUNGE-KUTTA METHODS
3.4. MATLAB ODE45 SOLVER: OPTIONS AND PARAMETERIZATION
3.5. CASE STUDIES AND EXAMPLES
CHAPTER 4 PARTIAL DIFFERENTIAL EQUATIONS IN TIME
4.1. GENERAL SETUP
4.2. A BRIEF OVERVIEW OF NUMERICAL METHODS
4.3. HYPERBOLIC PDE: CONVECTIVE SYSTEMS
4.4. PARABOLIC PDE: DIFFUSIVE SYSTEMS
4.5. CASE STUDIES AND EXAMPLES
CHAPTER 5 SECTION WRAP-UP: SIMULATION AND ANALYSIS
5.1. BINARY DISTILLATION COLUMN: STAGED ODE MODEL
5.2. STABILITY ANALYSIS FOR LINEAR SYSTEMS
5.3. COMBINED PARABOLIC PDE WITH ODE-IVP: POLYMER CURING
5.4. TIME VARYING INLET CONDITIONS AND PROCESS DISTURBANCES
5.5. SIMULATING SYSTEM WITH BOUNDARY CONSTRAINTS
CHAPTER 6 NONLINEAR ALGEBRAIC EQUATIONS
6.1. GENERAL SETUP
6.2. EQUATIONS IN SINGLE VARIABLE
6.3. NEWTON-RAPHSON: EXTENSIONS AND MULTI-VARIATE
6.4. MATLAB SOLVERS
6.5. CASE STUDIES AND EXAMPLES
CHAPTER 7 SPECIAL METHODS FOR LINEAR AND NONLINEAR EQUATIONS
7.1. GENERAL SETUP
7.2. TRI-DIAGONAL AND BANDED SYSTEMS
7.3. ITERATIVE METHODS
7.4. NONLINEAR BANDED SYSTEMS
CHAPTER 8 IMPLICIT METHODS: DIFFERENTIAL AND DIFFERENTIAL ALGEBRAIC SYSTEMS
8.1. GENERAL SETUP
8.2. MULTI-STEP METHODS FOR DIFFERENTIAL EQUATIONS
8.3. IMPLICIT SOLUTIONS FOR DIFFERENTIAL EQUATIONS
8.4. DIFFERENTIAL ALGEBRAIC EQUATIONS (DAES)
8.5. CASE STUDIES AND EXAMPLES
CHAPTER 9 SECTION WRAP-UP: NONLINEAR ANALYSIS
9.1. NONLINEAR ANALYSIS OF CHEMOSTAT: "TRANSCRITICAL" BIFURCATION
9.2. NON-ISOTHERMAL CSTR: "TURNING-POINT" BIFURCATION
9.3. LIMIT CYCLE OSCILLATIONS
9.4. SIMULATION OF METHANOL SYNTHESIS IN TUBULAR REACTOR
9.5. TRAJECTORY OF A CRICKET BALL
CHAPTER 10 REGRESSION AND PARAMETER ESTIMATION
10.1. GENERAL SETUP
10.2. LINEAR LEAST-SQUARES REGRESSION
10.3. REGRESSION IN MULTIPLE VARIABLES
10.4. NONLINEAR ESTIMATION
10.5. CASE STUDIES AND EXAMPLES
Dr. Niket Kaisare is currently an Associate Professor in the Department of Chemical Engineering at IIT-Madras. He obtained PhD in Chemical Engineering from Georgia Institute of Technology, working in model-based advanced process control. After a post-doc in the department of chemical engineering at University of Delaware, he joined IIT-Madras as Assistant Professor in 2007. While in IIT-Madras, he taught several courses in process modeling and analysis, computational techniques, process simulation laboratory, and advanced control theory. His courses have consistently gotten good student feedback.
He spent three years, from mid-2011 to 2014, in Industrial R&D. During this stint, he worked on numerous simulation problems related to modeling of vehicle catalytic convertors, cryogenic hydrogen storage, monitoring and control of oil and gas wells, and automation engineering. As a part of R&D team, he used MATLAB extensively and spent important fraction of his time interfacing with engineering and development teams.
He has extensive experience working in MATLAB and FORTRAN as well as simulation software Fluent and Comsol. He also has good working experience with various other simulation tools, such as Aspen-Plus / Unisim, Gaussian and Abacus. His current research program is focused on "multi-scale modeling, analysis and control of catalytic micro-reactors for energy and fuel processing applications."
- Introduction to MATLAB Programming for Numerical Computation by Dr. Niket Kaisare