Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Stability condition for solving convection equation by FDM

  1. May 25, 2015 #1

    I know, there is a stability condition for solving the Convection-Diffusion equation by Finite Difference explicit/implicit technique, which is \Delta t<=(\Delta x)^2/(2*D) for one-dimensional or \Delta t<=((\Delta x)^2+(\Delta y)^2)/(8*D) for two-dimensional problem, where D is the diffusion coefficient.
    Is there any such condition for only the convection equation?

  2. jcsd
  3. May 27, 2015 #2
    The stability criterion is dependent on your FD approximation of the laplacian. Have you tried calculating the stability conditions? I am not sure why the same method wouldn't work for the convection term. I have not done it for the convection though.
  4. May 27, 2015 #3
    Thanks for your response. I am not sure how to calculate the stability condition. I have used the the formula \Delta t<=((\Delta x)^2+(\Delta y)^2)/(8*D) to make my program stable. But if there is no diffusion term,only convection term, how will I calculate the stability condition?

  5. May 28, 2015 #4
    After some thought I am not even sure you can do the calculation with the convection term, since the stability of the diffusion equation is calculated using a fourier series. Unless the velocity is constant i suppose things will not work that well.
    Further more as far as I remember just advecting a field is not so easy numerically due to various problems(at least not in the long time limit). What are you advecting by the way? An interface? This article discusses a bit about passiv advection

    I think it is nice enough.(and eq 2 might be what you are looking for).
  6. May 28, 2015 #5
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook