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In [[computational fluid dynamics]], the '''projection method''', also called '''Chorin's projection method''', is an effective means of [[Numerical analysis|numerically]] solving time-dependent [[incompressible flow|incompressible fluid-flow]] problems. It was originally introduced by [[Alexandre Chorin]] in 1967<ref>
{{Citation
| surname1 = Chorin
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| volume = 73
| year = 1967
| issue = 6
| pages = 928–931
| doi = 10.1090/S0002-9904-1967-11853-6
| url =http://math.berkeley.edu/~chorin/chorin67.pdf
}}</ref><ref>
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| volume = 22
| year = 1968
| issue = 104
| pages = 745–762
| url =
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| doi-access = free
}}</ref>
as an efficient means of solving the incompressible [[Navier-Stokes equation]]s. The key advantage of the projection method is that the computations of the [[Flow velocity|velocity]] and the pressure fields are decoupled.
==The algorithm==
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==Helmholtz–Hodge decomposition==
The theoretical background of projection type method is the decomposition theorem of [[Olga Aleksandrovna Ladyzhenskaya|Ladyzhenskaya]] sometimes referred to as Helmholtz–Hodge Decomposition or simply as Hodge decomposition. It states that the vector field <math>\mathbf{u}</math> defined on a [[simply connected space|simply connected]] ___domain can be uniquely decomposed into a divergence-free ([[Solenoidal vector field|solenoidal]]) part <math>\mathbf{u}_{\text{sol}}</math> and an [[Conservative vector field#Irrotational vector fields|irrotational]] part <math>\mathbf{u}_{\text{irrot}}</math>.
Thus,
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