# What is Method of Characteristics?

I am a final year student of BS Mechanical Engineering and method of characteristics is not a part of our curriculum. In-fact I heard of it first time after finally picking my FYP. My final year project is to design analyze and manufacture a CD Nozzle which would achieve Mach 3. I was told by my supervisor that I would have to build the profile of the nozzle using method of characteristics because he wants the profile to be generalized so that every time the inlet condition changes, the profile changes automatically. My supervisor who himself is only a doctorate has never studied MOC himself so he can not help me. I want to know what it is and how could I start practicing it. Moreover what are the pre-requisites to start learning it. Any help would highly be appreciated.

• Would Mathematics be a better home for this question? Commented Aug 17, 2015 at 20:23
• Any good textbook on supersonic flow should discuss the method of characteristics. Commented Aug 17, 2015 at 21:39
• see this for a simple example: physics.stackexchange.com/q/439877/226902 and this for a very nice tutorial scottsarra.org/shock/shock.html#moc Commented Jan 11, 2023 at 17:37

I see that your goal is to design a supersonic nozzle. I will answer your questions with that in mind.

I want to know what it is

It is a method for solving hyperbolic partial differential equations.

In the case of supersonic flow, the method of characteristics defines paths through the flow for which certain quantities are known (or easily calculated).

and how could I start practicing it. Moreover what are the pre-requisites to start learning it.

First, one should know some fluid mechanics, particularly the conservation equations for mass, momentum, and energy. Next, one should study supersonic flow enough to understand both shock waves and expansion fans. Solution of supersonic flow via method of characteristics should be included in any good textbook on supersonic flow. A classic supersonic flow textbook is Compressible Fluid Flow by Ascher H Shapiro. Method of characteristics is discussed in Chapter 15 of Volume 1. Some short sections on method of characteristics can also be found in Fluid Mechanics by Landau and Lifshitz.

I just found that second volume of Gas Dynamics by Zucrow wholly deals with the use of Method of Characteristics to solve various kinds of flow problems. I hope it will solve my problem.