Incompressible NavierStokes Equation

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Incompressible Navier-Stokes Equation

• 2004-4-18

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Non-dimensionalization
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Primitive Variable Formulations ? Two
dimensional (CONSERVATIVVE FORM)
? Non-dimensional (CONSERVATIVVE FORM)
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Vorticity-Stream Function Formulation
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O
Continuity eqn.
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Vorticity-Stream Function Formulations
?Dimensional CONSERVATIVVE FORM
? Non-dimensional (CONSERVATIVVE FORM)
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? Primitive variable formulation i) A mixed
elliptic-parabolic equn. ( two unknowns
pressure, velocity ) ii) no direct link for
the pressure between continuity momentum equn.
? Poisson equn. for pressure ?
Vorticity-Stream function formulation i)
vorticity-stream function formulation does not
include the pressure term. ? the velocity
field is determined initially ? For the
pressure field, Poisson equn. ii) The lack of
al simple stream function in three diminsions
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Poisson Equation for Pressure ?Primitive
Variables
addition
0 continuity equn.
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For an incompressible flow, D0 However, due to
numerical consideration, this term will not be
set to zero It must be evaluated to prevent error
accumulation, as well as to prevent nonlinear
instability
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Poisson Equation for Pressure ?Vorticity-Stream
function formulation