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{{Short description|Method for numerically solving time-dependent incompressible fluid-flow problems}}
In [[computational fluid dynamics]],
{{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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==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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