Numerical Methods in Chemical Engineering with Finite Difference Discretization

Chemical engineering transport phenomena and reaction systems often rely on differential equations that cannot be solved analytically. This course introduces you to the foundational concepts of numerical discretization, enabling you to transform complex differential equations into solvable algebraic systems. You will learn to construct, analyze, and implement numerical approximations that are critical for simulating fluid flow, heat transfer, and mass transport processes. By working through this structured text-only material, you will transition from understanding theoretical transport equations to writing clear, logical code that solves them numerically. You will gain a solid grasp of how grid spacing, stability, and boundary conditions affect your simulation results. What you'll learn: - Understand the core mathematical theory behind finite difference approximations of first and second derivatives - Build spatial discretization matrices for one-dimensional grids using central and upwind difference schemes - Apply appropriate boundary conditions to close numerical systems of equations - Analyze numerical stability and numerical diffusion to choose the right discretization scheme for transport problems - Configure system matrices and vector formulations to solve steady-state and transient engineering problems The course begins with foundational definitions of discretization, grid generation, and Taylor series expansions. From there, you will progress through structured derivations of central and upwind schemes, explore stability criteria, and read through practical code implementations for chemical engineering transport equations. This course is designed for chemical engineering students, researchers, and practicing engineers who want a clear, step-by-step introduction to numerical methods without complex prerequisites beyond basic calculus and introductory programming concepts. Start mastering the numerical techniques that power modern chemical process simulation.