1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: PDE Help! = Characteristic Curves / Method of Characterization

  1. Oct 24, 2011 #1
    1. Show that, if the velocity field (V) is a fixed (spatially constant) vector, then the characteristic curves will be a family of parallel-straight lines.



    2. ut+V1ux+V2uy=f
    f=S-[dell dotted with V]u

    characteristic curves:
    dX/dt=V1(X,Y) & dY/dt=V2(X,Y)


    3. really looking for help on how to get started on this. any suggestions would be appreciated.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Oct 25, 2011 #2
    Since V is fixed (i.e. [itex]V_1(x,y) = C_1; V_2(x,y) = C_2[/itex], you can solve the parametric equations for the characteristic curves explicitly, and obtain X(t), and Y(t). What types of curves are these?
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook




Loading...