Numerical Methods for Partial Differential Equations in Chemical Engineering

In chemical engineering, physical processes like heat transfer, mass diffusion, and fluid flow are governed by partial differential equations (PDEs). Understanding how to set up, discretize, and solve these equations numerically is essential for designing and optimizing chemical systems. This course provides a clear, text-based path to mastering numerical methods for PDEs, translating complex physical phenomena into solvable computer models. You will transition from theoretical transport equations to robust numerical simulations, learning how to select the right algorithms for different engineering scenarios. Through detailed explanations and step-by-step code walkthroughs, you will develop a deep intuition for mathematical modeling. What you'll learn: - Understand the classification of PDEs and their physical relevance to transport phenomena - Apply finite difference methods to discretize spatial and temporal derivatives - Implement implicit and explicit numerical schemes to solve diffusion and convection equations - Analyze numerical stability and convergence using modern computational practices - Model real-world chemical engineering systems, including reactor dynamics and heat exchangers The course begins with foundational mathematical definitions and the classification of PDEs before moving into spatial discretization, time-stepping algorithms, stability analysis, and multi-dimensional transport systems. Every concept is reinforced with clean code snippets and written exercise problems. This course is designed for undergraduate students, graduate researchers, and practicing chemical engineers who have a basic background in calculus and programming and want to build a strong foundation in numerical modeling. No advanced mathematical background is required. Start modeling complex chemical engineering transport systems today.