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