Level set method for droplet simulation
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The document summarizes the level set method for simulating droplets. It describes using the level set method to represent the interface as the zero level set of a function φ. The interface moves with the fluid particles according to the Navier-Stokes equation. Surface tension is modeled as a body force localized on the interface. Density and viscosity are constant in each region. Dimensionless equations are derived and the projection method is used to handle high Reynolds number flows. The thickness of the interface is defined based on a smoothed Heaviside function.
Level set method for droplet simulation
- 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.