# non-staggered fractional step method

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 December 10, 2007, 11:59 non-staggered fractional step method #1 shyam Guest   Posts: n/a hi all, I am working in the simulation of incompressible fluid flows. can any one suggest me a very good reference for implementing fractional step method in non-staggered grids? Thanking you,

 December 12, 2007, 05:43 Re: non-staggered fractional step method #2 Quarkz Guest   Posts: n/a Hi, You can try "A Second-Order Time-Accurate Finite Volume Method for Unsteady Incompressible Flow on Hybrid Unstructured Grids" by Choi. JCP 162,411-428(2000)

 October 25, 2009, 09:47 Easy Implementation of FSM #3 New Member   Eduardo Hwang Join Date: Oct 2009 Posts: 1 Rep Power: 0 Hi, This may be a bit late for the original post, but I hope it helps other people. A nice way to implement FSM for incompressible flows, either in structured or unstructured meshes (FVM or FEM) is to derivate the Navier-Stokes in 3-D, in the x direction regarding the x coordinate, the y direction for the y coordinate, and so for z. You will notice that in these three lines of equations, the pressure gradient in each one has now become a second derivative of pressure P. By adding the 3 equation lines, one obtains a Laplacian of P, and therefore a Poisson Equation emerges. The right-hand side of this equation is simply the gradient of the velocity error (namely, the velocity without the pressure contributions), respective to each direction (remember that you derivated NS eq. regarding x,y,z). Now, one must prescribe the pressure boundary conditions in the linear system and solve it. Voilą, now you got the pressure correction for your velocity field. The only thing I am not really sure about, is the spatial accuracy order. To me it seems to depend on how one specifies the BCs, and the effective discretization of the Laplacian (ie. shape function for Finite Element).

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