# Fractional step in ALE form - possible?

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 September 29, 2006, 23:07 Fractional step in ALE form - possible? #1 Wee Guest   Posts: n/a hello, i'm using the fractional step on a structured grid to solve flow past a cylinder. discretization is based on FVM, CN2 for viscous, AB2 for convective term. the non-dimensionalized eqns in integral form are: f[ (u(*)-u(n))/dt ]dV + f[ 1.5*u(n)*U(n)-0.5*u(n-1))*U(n-1)) ]dS = 0.5*f[ L(u(n)+u(*)).n ]dS /Re f[ dp/dn ]dS = f[ U(*).n ]dS /dt u(n+1)=u(*)- dt*(G(p)) (cc) U(n+1)=U(*)- dt*(dp/dn) (fc) f[ ] is the integration summation U is the face normal velocity, u is the cell center L is the discrete laplace operator, G is the discrete gradient. cc mean G(p) is evaluated at the cell center fc mean dp/dn is evaluated at the face center to prevent pressure oscillation. i intent to modified it to the ALE (Arbitrary Lagrangian-Eulerian) form to simulate oscillating cylinder. searching the net shows that a lot of ppl use FEM or FVM with artificial compressibility. there are some who use SIMPLE/FVM with ALE. however i can't seem to find ppl using ALE in fractional step. i wonder why? is it just preference or...? from my understanding, the main modification in the ALE form is the convective velocity, which in this case is the changing of U (face normal velocity) to U - Ub, where Ub is the face normal mesh velocity. hence, the overall change is only in the momentum and poisson eqn, where all the U will become U - Ub. also, the change in BC will be wall velocity from 0 to cylinder velocity, that's all. with these modification, i'll be able to simulate oscillating cylinder.

 September 30, 2006, 18:47 Re: Fractional step in ALE form - possible? #2 Mani Guest   Posts: n/a I suppose you'll have to define some grid velocity associated with the intermediate position (*). Also, in the case of a deforming grid, don't forget that dV belongs inside the time derivative term (you may not need this if your cylinder grid is rigid).

 October 3, 2006, 10:20 Re: Fractional step in ALE form - possible? #3 Wee Guest   Posts: n/a hmm... i just tried moving the whole grid to simulate the oscillating cylinder but the answer's not correct. BC for (*) is supposed to be at t=n+1, so the grid velocity is the one at t=n+1. other than that, i don't see any other changes required. Btw, i found that the lift/drag coefficient computed using tecplot and my own extrapolation subroutine are different, both in value and frequency, although both are wrong anyway. strangely, for sll other cases (stationary,rotating,unsteady), the cl/cd are quite similar. i believe there's no need to modify my cl/cd formula for the . that's what i was told in another post.

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