**Numerical Solutions Applied To Heat Transfer And
Fluid
Mechanics Problems**

At this point you can create finite difference and finite volume equations, and solve them in the context of steady state problems. As I said in class, the really interesting problems are transient. Even problems that you consider to be steady state actually have transient aspects such as vortex shedding that should be considered. I'm going to introduce transient solution methods within the familiar context of the conduction equation. However, you learn most of what you need to know to solve a wide range of other problems. We will follow with discussions of fluid flow.

These lectures cover the following general topics:

- Forward (Explicit) Difference Methods
- Basics of Stability Limits
- Backward (Implicit) Difference Methods
- ADI Methods

Following these topics we take a look at von Neumann (Fourier) stability analysis. This will be done in the context of flow (advection) equations.