Numerical Methods for Internal Aerodynamics
1. Historical Background:
This topic covers what we think of as CFD (Computational Fluid Dynamics). It walks through the building blocks of solvers. Then, go over the historical development and key milestones in the field. This introductory section is organized into
2. Finite Difference Method:
This topic starts by deriving the mass flow rate equation leading to the conservation law. Discusses hyperbolic equations and the difference quotient approach for approximating derivatives. It emphasizes the importance of the Taylor series expansion in deriving finite difference approximations and defines the convenient Big-O notation for truncating the series. Then, the order of approximation is introduced and a summary of the material covered is provided. The lectures are organized as follows:
3. Finite Volumes Method:
In this topic, finite volumes is introduced from average cell volumes, and the upwinding scheme is introduced. Continuing the development of the main model, the momentum equation is derived. Then, the incompressible Navier–Stokes equations is presented. Relevant to internal aerodynamics, laminar boundary layers are introduced. Lastly, solution stratigies for the Navier–Stokes are introduced, comparing the density and pressure based solvers. This topic is the laregest section of the course, covering:
- systems of conservation laws,
- finite volumes method,
- the momentum equation,
- incompressible flow,
- laminar boundary layers, and
- solution strategies.
4. Time Integration Methods:
The last main topic starts by discussing the difference between Partial Differential Equations (PDEs) and Ordinary Differential Equations (ODEs). Explicit time integration is introduced first. Then, stability and stiffness are discussed. Through the connection betwee stability and stiffness, implicit time integration is introduced. The lectures are organized as follows: