Difference between finite volume, characteristic method and plug flow models of a pipe I have to model pipes (of a district heating network) with ODE's.
My background is computer-science, so it is not that easy for me to understand different approaches.


*

*Finite volume approach.

*Method of characteristics.

*Plug-Flow model of a pipe.
I don't have to understand each approach in detail - but it would help a lot to have a good overview. Some in my group think, that the method of characteristics is the same as the plug-Flow approach, is that true?
Would be really great, if someone could help.
 A: The Finite Volume Method, and Method of Characteristics are both ways to go about solving partial differential equations.
The Finite Volume Method is a way to take complicated geometry that would be impossible or difficult to model analytically and break it into regions that adhere to geometry that is easy to model analytically such as tetrahedrons. The partial differential equations are solved on these simple geometries and then the boundary conditions knit them together.
The Method of Characteristics is an analytical method of transforming partial differential equations into forms that are easily solved. This requires the original problem to be posed analytically. This method could be used to solve the simple geometries produced by the finite volume method.
Plug Flow is a method that is specific to flow of fluids through pipes. It makes the assumption that a pipe can be treated as one dimensional, and the internals of a given cross section can be abstracted away. For example rather than having a velocity vector field, and a temperature field for every cross sectional slice of the pipe, you can simplify each cross section down to a point such that you only have an average velocity, an area, and a temperature at each point along a pipe.
All three of these methods could be combined, for example, your pipes could be segmented (Finite Volume Method) into constant area sections, and joints, which could each be modeled using an analytical plug flow PDE using the method of characteristics.
