# Question regarding non-uniform FVM staggered grid and order accuracy

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 October 25, 2012, 09:56 Question regarding non-uniform FVM staggered grid and order accuracy #1 Senior Member   TWB Join Date: Mar 2009 Posts: 105 Rep Power: 8 Hi, I have a question regarding non-uniform FVM staggered Cartesian grid and order accuracy. When the grid is non-uniform, I define the u,v,p grids such that the east/west faces of the u grid intersects the cell center of p. Same for the v grid. In that case, the distance of the east/west faces from the cell center of u will be different. the volume of u and p cells are different. When using the fractional method, after evaluating the pressure from the Poisson eqn, to get u velocity, I use: u(n+1) - u(*) = -(delta_t / vol) * pressure(east face) -pressure(west face) * area, where u*) is the intermediate velocity However, since my u value is not at the center of the cell, it will not give a 2nd order solution, is that so? How can I resolve this? Thanks

October 25, 2012, 11:22
#2
Senior Member

Filippo Maria Denaro
Join Date: Jul 2010
Posts: 1,601
Rep Power: 23
Quote:
 Originally Posted by quarkz Hi, I have a question regarding non-uniform FVM staggered Cartesian grid and order accuracy. When the grid is non-uniform, I define the u,v,p grids such that the east/west faces of the u grid intersects the cell center of p. Same for the v grid. In that case, the distance of the east/west faces from the cell center of u will be different. the volume of u and p cells are different. When using the fractional method, after evaluating the pressure from the Poisson eqn, to get u velocity, I use: u(n+1) - u(*) = -(delta_t / vol) * pressure(east face) -pressure(west face) * area, where u*) is the intermediate velocity However, since my u value is not at the center of the cell, it will not give a 2nd order solution, is that so? How can I resolve this? Thanks

I suggest to see the dedicated part in:

http://onlinelibrary.wiley.com/doi/1...d.613/abstract
http://onlinelibrary.wiley.com/doi/1...al+maintenance

 October 26, 2012, 03:11 #3 Senior Member   TWB Join Date: Mar 2009 Posts: 105 Rep Power: 8 Thanks Filippo, I'll take a look at them.

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