level set method for droplet simulation
DESCRIPTION
TRANSCRIPT
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Level set method for Droplet Simulation
Jong su, Kim
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Equation of Motion
Navier stokes equation for Incompressible flow
Boundary Condition.
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Level set method
The interface is the zero level set of 𝜙
Take 𝜙 < 0 in the gas region and 𝜙 > 0 in the liquid region.
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Level set method
Define
Since the inteface moves with the fluid particles, then we can get
Surface tension force is interpreted as a body force localized on the interface
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Density and viscosity are constant in each field, define
Where 𝐻(𝜙) is the Heaviside function given by
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Dimensionless form
+
Prime ′ means dimensionless
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Dimensionless form
Gravity is −𝑦 direction
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Projection Method
Use projection scheme coupled with high order upwind differencing of the convective terms in torder to handle high Reynolds number flow
Hodge decompsition
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Thickness of the interface
To Solve
Modify
to (Smooth density)
with
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Thickness of the interface
From
Thickness is
Assume
Define function
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View level set function as distance function
Function d
Thickness is
Take
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To solve this, solve the following partial differential equation.
View level set function as distance function
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During simulation, volume cannot be retained. To correct this, add this equation.
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Overall Algorithm