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!

What does the Navier-Stokes equation look like after time discretization?

  1. Dec 2, 2016 #1

    I know the general form of the Navier Stokes Equation as follows.

    I am following a software paper of "Gerris flow solver written by Prof. S.Popinet"
    and he mentions after time discretization he ends with the following equation:
    where n-1 is the previous time step, n+1 is the next time step and n+0.5 is mid time for the present time step.

    Solving equation implicitly/ explicitly in time means solving for next time data however in the equation there are rather two unknowns un+0.5 and

    Not sure why he uses different terms at different time intervals. Density at n+0.5, velocity at n, n-1, n+0.5 etc..

    Can anyone point me or explain me how he arrives at this specific sort of discretized equation.
  2. jcsd
  3. Dec 2, 2016 #2
    The link to the paper doesn't work.
  4. Dec 2, 2016 #3
    I'm not familiar with this particular finite difference scheme, but presumably un+0.5 is already know when you are calculating un+1
  5. Dec 2, 2016 #4
    Sorry for the link.

    @Chestermiller guess thats true. It is being solved by the time step projection method which means an intermediate velocity is computed and later updated to a divergence free velocity by solving the laplace of pressure term as in the mentioned paper.

    The notation is a bit strange for me as he uses density at time n+0.5 without solving any advection equation. From what I see density terms at n and n+0.5 should be the same.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted