1. Level set method for
Droplet Simulation
Jong su, Kim

2. Equation of Motion
Navier stokes equation for Incompressible flow
Boundary Condition.

3. Level set method
The interface is the zero level set of ������
Take ������ < 0 in the gas region and ������ > 0 in the liquid region.

4. 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

5. Density and viscosity are constant in each field, define
Where ������(������) is the Heaviside function given by

6. Dimensionless form
+
Prime ′ means dimensionless

7. Dimensionless form
Gravity is −������ direction

8. 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

9. Thickness of the interface
To Solve
Modify
to (Smooth density)
with

10. Thickness of the interface
From
Thickness is
Assume
Define function

11. View level set function as distance function
Function d
Thickness is
Take

12. View level set function as distance function
To solve this, solve the following partial differential equation.

13. During simulation, volume cannot be retained.
To correct this, add this equation.

14. Overall Algorithm