Hello CFD Gurus I have doubt related to characteristics namely how many characteristics of a governing euation are possible?

Thanks in advance

for a general discussion of characteristics any good intro book on cfd like john anderson's or tannehill, anderson, and pletcher's can help you out. as for the number of characteristics an equation can have we can take the example of the euler equations in 3-d. we know from analysis that there are five characteristics in each direction ( ui+c, ui-c, ui,ui,ui where ui is the velocity component in the i direction). typically a system of equations has as many characteristics as the order of the highest time derivative times the number of equations in the systems * the number of coordinate directions. so the euler equations have 1*5*3 characteristics. another example is the scalar wave equation d^2u/dt^2=c^2(d^2u/dx^2+d^2u/dy^2+d^2u/dz^2) which has six characteristics which are -c and +c in each direction .and of course an equation can have different character in different directions ie in one direction it can be hyperbolic (wavelike) while it can be parabolic (diffusive) in another direction

Hi again there,

I see that you are taking classes with us...

If you want an insight into the characteristics, just have a look at a past message on

Riemann Invariants

in this same forum and you'll find out more about what you want.

Cheers,

Patrick

Dear Mr. Patric I am sorry if u have minded it. Actually i have just started in the field of CFD. I am reading books and literature and therefore i get doubts. Somehow i have found that people like u and Mr.john explain very nicely. That is the reason i ask questions like this. Hope u will cooperate in future also.

with regards

---kumar

Hi Kumar,

You are welcome! It is a pleasure to answer.

Patrick

Hi Mr.Patric Thank you very much