Level set method for Droplet Simulation
Jong su, Kim
Equation of Motion
Navier stokes equation for Incompressible flow
Boundary Condition.
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.
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
Density and viscosity are constant in each field, define
Where 𝐻(𝜙) is the Heaviside function given by
Dimensionless form
+
Prime ′ means dimensionless
Dimensionless form
Gravity is −𝑦 direction
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
Thickness of the interface
To Solve
Modify
to (Smooth density)
with
Thickness of the interface
From
Thickness is
Assume
Define function
View level set function as distance function
Function d
Thickness is
Take
To solve this, solve the following partial differential equation.
View level set function as distance function
During simulation, volume cannot be retained. To correct this, add this equation.
Overall Algorithm