Results 1 to 3 of 3

Math Help - Arakawa's C grid

  1. #1
    Junior Member
    Joined
    Oct 2009
    Posts
    31

    Arakawa's C grid

    Hi all,

    I'm stuck with how to define u

    given

    \frac {\partial u}{\partial x}\approx \frac{u_{i+1,j}-u_{i-1,j}}{2\Delta x}

    say I'm incrementing \Delta x and \Delta y at some defined value. I should have a 2D grid with x_{i} and y_{j} down either side and the central values will be u_{i,j}.

    How do I calculate u?

    Is it simply u_{i,j}=\frac{\partial x_{i}}{\partial t_{n}}+\frac{\partial y_{j}}{\partial t_{n}}

    where t_{n} is defined as n\Delta t
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,423
    Thanks
    1331
    Quote Originally Posted by davefulton View Post
    Hi all,

    I'm stuck with how to define u

    given

    \frac {\partial u}{\partial x}\approx \frac{u_{i+1,j}-u_{i-1,j}}{2\Delta x}

    say I'm incrementing \Delta x and \Delta y at some defined value. I should have a 2D grid with x_{i} and y_{j} down either side and the central values will be u_{i,j}.

    How do I calculate u?

    Is it simply u_{i,j}=\frac{\partial x_{i}}{\partial t_{n}}+\frac{\partial y_{j}}{\partial t_{n}}

    where t_{n} is defined as n\Delta t
    I'm not sure what you want here. u is simply some function that is defined at each node of grid. u_{i,j} is the value of that function at the i,j-node. It is NOT a derivative, it is the function itself. \frac{u_{i+1,j}-u_{i-1,j}}{2\Delta x} is an approximation to \frac {\partial u}{\partial x} on that grid and, similarly, \frac{u_{i,j+1}-u_{i,j-1}}{2\Delta y} is an approximation to \frac {\partial u}{\partial y}.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Oct 2009
    Posts
    31
    u is a velocity component. As is v. I'm using to solve Euler's equations.

    \frac{\partial u}{\partial x}\approx \frac{u_{i+1,j}-u_{i,j}}{\Delta x}

    \frac{\partial v}{\partial y}\approx \frac{v_{i,j+1}-v_{i,j}}{\Delta y}

    Thank you for your help
    Last edited by davefulton; January 31st 2010 at 03:04 PM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Ten by Ten grid
    Posted in the Discrete Math Forum
    Replies: 3
    Last Post: November 2nd 2009, 02:50 PM
  2. nxn grid problem.
    Posted in the Math Topics Forum
    Replies: 4
    Last Post: October 31st 2009, 07:00 AM
  3. grid of stairs
    Posted in the Algebra Forum
    Replies: 11
    Last Post: August 13th 2009, 05:55 AM
  4. Help With A Grid
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: October 31st 2008, 12:34 PM
  5. grid dots
    Posted in the Discrete Math Forum
    Replies: 0
    Last Post: April 17th 2007, 09:13 AM

Search Tags


/mathhelpforum @mathhelpforum