Level Set Method
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The document describes a level set method for simulating droplets using a Navier-Stokes equation. It defines the level set function φ such that φ<0 in the gas region and φ>0 in the liquid region. The interface is defined as the zero level set of φ. Density and viscosity are defined as constant in each region using the Heaviside function of φ. Dimensionless forms of the equations are presented. A projection method is used to handle high Reynolds number flows. The level set function is modified to have a smooth density and a thickness at the interface defined using a function of φ. An equation is added to correct volume during simulation.
Level Set Method
- 1. Level set method for Droplet Simulation Jong su, Kim
- 3. Equation of Motion Navier-stokes equation for Incompressible flow Boundary Condition
- 5. < 0 = 0 > 0
- 6. Level Set Method The interface is the zero level set of Take < 0 in the gas region and > 0 in the liquid region.
- 7. Level set method Define Since the interface moves with the fluid particles, then we can get Surface tension force is interpreted as a body force localized on the interface
- 8. Level set method Density and viscosity are constant in each field, define Where () is the Heaviside function given by
- 9. Dimensionless form + Prime ′ means dimensionless
- 10. Dimensionless form Gravity is − direction
- 11. Projection method Use projection scheme coupled with high order upwind differencing of the convective terms in order to handle high Reynolds number flow Hodge decomposition Therefore.. It eliminates pressure
- 12. Thickness of surface To Solve Modify to (Smooth density) with
- 13. Thickness of the interface From Thickness is Assume Define function
- 14. View level set function as distance function Function d Thickness is Take
- 15. View level set function as distance function To solve this, solve the following partial differential equation.
- 16. During simulation, volume cannot be retained. To correct this, add this equation.