Advancements in Two-Phase Flow Simulation: A Focus on Level-Set Methods

1. A review of level-set methods for two-phase flows Arthur Kerst 1

2. Overview Introduction • Introduction • Goal of project • Overview of methods • Conclusion Goal of project Overview of methods Conclusion 2

3. Introduction Introduction • Two-phase flow • Fundamental tools in many industrial applications and natural processes • Far more challenging than single phase flow • Volume conservation and accurately modelling the interface Goal of project Overview of methods Conclusion 3

4. Goal of project Introduction Goal: develop a method using a continuous Galerkin approach for solving the level-set equation on triangular control volumes Goal of project Overview of methods Conclusion • conserve volume exactly • continuous description of the interface • track interface accurately • able to handle unstructured triangular grids 4

5. Overview of methods Introduction • Front-tracking methods • Marker-and-cell methods • Level-set (LS) methods • Volume-of-fluid (VoF) method Goal of project Overview of methods no geometrical restrictions Conclusion 5

6. Volume-of-fluid method Introduction Colour function Goal of project Overview of methods Conclusion Volume fraction Advection 6

7. Volume-of-fluid method Introduction Goal of project Overview of methods Conclusion 7

8. Volume-of-fluid method Rotating flow with Lagrangian-Eulerian advection method. Introduction Goal of project Overview of methods Conclusion 8

9. Volume-of-fluid method Introduction • Advantages – Volume conservation • Disadvantages – Computationally intensive interface reconstruction – Discontinuous interface Goal of project Overview of methods Conclusion 9

10. Level-set method Introduction Signed-distance function Goal of project Overview of methods Conclusion Advection 10

11. Level-set method Introduction Goal of project Overview of methods Conclusion 11

12. Level-set method Rotating flow with SUPG method and Crank-Nicolson scheme. Introduction Goal of project Overview of methods Conclusion 12

13. Level-set method Introduction • Advantages – Continuous interface – Geometrical information can be easily calculated • Disadvantages – Volume loss/gain – Instabilities – Reinitialization Goal of project Overview of methods Conclusion 13

14. Improvements to the level-set method Introduction • Improving LS discretization and reinitialization • Hybrid methods • Volume correction methods • Modified level-set formulation Goal of project Overview of methods Conclusion 14

15. Hybrid methods Introduction • Hybrid methods with VoF – Coupled level-set and volume-of-fluid (CLSVOF) method – The coupled volume-of-fluid and level-set (VOSET) method – The mass-conserving level-set (MCLS) method Goal of project Overview of methods Conclusion 15

16. The mass-conserving level-set (MCLS) method • Volume fraction construction Introduction Goal of project Overview of methods Conclusion • Advection of LS and VoF field – For VoF advection, information of LS function is used • Volume correction procedure 16

17. Advection of level-set method Introduction Standard Galerkin approach Goal of project Overview of methods Conclusion 17

18. Advection of level-set method Introduction Standard Galerkin approach with reinitialization Goal of project Overview of methods Conclusion 18

19. Advection of level-set method Introduction SUPG method Goal of project Overview of methods Conclusion 19

20. Conclusion Introduction • LS method gives continuous description of interface, but has no volume conservation • VoF is volume-conserving, but interface is discontinuous and interface reconstruction computationally intensive. • MCLS is a hybrid level-set method, which uses volume fractions for volume conservation, without the expensive interface reconstruction step. • A stabilization method is needed for LS advection. Goal of project Overview of methods Conclusion 20

21. Further research Develop a hybrid method with LS and VoF similar to MCLS with a continuous FEM approach. – How well does SUPG combines with VoF? – Is SUPG sufficiently accurate (for maintaining shape)? – What is necessary to successfully and efficiently implement this? An appropriate volume correction procedure must be chosen or developed. Is reinitialization necessary? Which temporal scheme is best suited for LS advection? • Introduction Goal of project Overview of methods Conclusion • • • 21

22. End of presentation 22