MAE 5100

Numerical Methods for Fluids: From Foundations to AI-Enhanced CFD

Course Description

Course information provided by the 2025-2026 Catalog.

This course introduces the numerical methods and computational techniques for solving partial differential equations (PDEs) in fluids, heat transfer, and related transport phenomena. Students will study model PDEs to develop a rigorous foundation in discretization, truncation error, stability, and convergence. Core topics include finite difference and finite volume methods, explicit and implicit time-marching schemes, and iterative solvers for large linear systems. A distinctive emphasis is placed on the hands-on development of numerical solvers: students will implement algorithms in Python to simulate canonical problems (convection, diffusion, Poisson, Burgers equations) and extend them to the Navier–Stokes equations. Advanced modules introduce next-generation methods such as GPU acceleration, differentiable programming, and hybrid AI–PDE solvers. The course emphasizes algorithmic and computational foundations rather than commercial software.

Prerequisites MAE 3230 or equivalent, Python programming knowledge.

Last 4 Terms Offered (None)

Learning Outcomes

• Derive and explain numerical methods such as finite difference and finite volume schemes, and assess their order of accuracy.| Analyze the stability, consistency, and convergence of discretization methods for PDEs arising in fluids and thermal transport.| Implement and verify numerical solvers in Python, and demonstrate their application to canonical PDEs and the Navier–Stokes equations.

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