Development of level set method with good area preservation to predict interface in two-phase flows

International Journal for Numerical Methods in Fluids

Volumn 67, Issue 1, 2011, Pages 109-134

  Sheu, Tony W H ^a   Yu, C H ^a   Chiu, P H ^a  

^a NATIONAL TAIWAN UNIVERSITY   (Taiwan)

Author keywords

Area preservation; Casimir; Conservative level set method; Coupled compact scheme; Dispersion relation preserving; Hamiltonian; Sixth order accurate; Symplectic Runge Kutta

Indexed keywords

AREA PRESERVATION; CASIMIR; COMPACT SCHEMES; DISPERSION-RELATION-PRESERVING; LEVEL SET METHOD; SIXTH-ORDER ACCURATE; SYMPLECTIC;

ADVECTION; AIRCRAFT PROPULSION; DISPERSIONS; DROP BREAKUP; EQUATIONS OF MOTION; HAMILTONIANS; INCOMPRESSIBLE FLOW; LEVEL MEASUREMENT; NONLINEAR EQUATIONS; PHASE INTERFACES; RUNGE KUTTA METHODS; SET THEORY; TWO PHASE FLOW;

NUMERICAL METHODS;

EID: 79961081187     PISSN: 02712091     EISSN: 10970363     Source Type: Journal    
DOI: 10.1002/fld.2344     Document Type: Article

References (35)

1. Sethian JA, Adalsteinsson D. An overview of level set methods for etching, deposition and lithography development. IEEE Transactions on Semiconductor Manufacturing 1997; 10(1):167-184.
2. Anderson CR. A vortex method for flows with slight density variations. Journal of Computational Physics 1985; 61(3):417-444.
3. Boultone-Stone JM, Blake JR. Gas bubbles bursting at a free surface. Journal of Fluid Mechanics 1993; 254:437-466.
4. Hirt CW, Nichols BD. Volume of fluid method (VOF) for the dynamics of free boundaries. Journal of Computational Physics 1981; 39:201-225.
5. Unverdi S, Tryggvason G. A front-tracking method for viscous, incompressible, multi-fluid flows. Journal of Computational Physics 1992; 100:25-37.
6. Badalassi VE, Ceniceros HD, Banerjee S. Computation of multiphase systems with phase field models. Journal of Computational Physics 2003; 190:371-397.
7. Kim J. A continuous surface tension force formulation for diffuse-interface models. Journal of Computational Physics 2005; 204:784-804.
8. Ding H, Spelt PDM, Shu C. Diffuse interface model for incompressible two-phase flows with large density ratios. Journal of Computational Physics 2007; 226:2078-2095.
9. Sethian JA, Smereka P. Level set methods for fluid interfaces. Annual Review of Fluid Mechanics 2003; 35:341-372.
10. Hirt CW, Amsden AA, Cook JL. An arbitrary Lagrangian-Eulerian computing method for all flow speeds. Journal of Computational Physics 1997; 135(2):203-216.
11. Harlow F, Welch J. Volume tracking methods for interfacial flow calculations. Physics of Fluids 1965; 8:21-82.
12. Osher S, Sethian JA. Fronts propagating with curvature dependent speed: algorithms based on Hamilton-Jacobi formulation. Journal of Computational Physics 1988; 79:12-49.
13. Marchandise E, Remacle JF, Chevaugeon N. A quadrature-free discontinuous Galerkin method for the level set equation. Journal of Computational Physics 2006; 212:338-357.
14. Thomas PD, Lombard CK. Geometric conservation law and its application to flow computations on moving grids. AIAA Journal 1979; 17(10):1030-1037.
15. Sheu TWH, Chen YH. Numerical study of flow field induced by a locomotive fish in the moving meshes. International Journal for Numerical Methods in Engineering 2007; 69:2247-2263.
16. Enright D, Fedkiw R, Ferziger J, Mitchell I. A hybrid particle level set method for improved interface capturings. Journal of Computational Physics 2002; 183:83-116.
17. Sussman M, Fatermi E, Smereka P, Osher S. An improved level set method for incompressible two-fluid flows. Computers and Fluids 1988; 127:663-680.
18. Sussman M, Puckett E. A coupled level set and volume-of-fluid method for computing 3D and axisymmetric incompressible two-phase flow. Journal of Computational Physics 2000; 162:301-337.
19. Strain J. Tree methods for moving interfaces. Journal of Computational Physics 1999; 151:616-648.
20. Osher S, Fedkiw R. Level Set Methods and Dynamic Implicit Surfaces. Springer: Berlin, 2003.
21. Sethian JA. Level Set Methods and Fast Marching Method. Cambridge University Press: Cambridge, 2003.
22. Olsson E, Kreiss G. A conservative level set method for two phase flow. Journal of Computational Physics 2005; 210:225-246.
23. McLachlan RI. Area preservation in computational fluid dynamics. Physics Letters A 1999; 264:36-44.
24. Chu PC, Fan C. A three-point combined compact difference scheme. Journal of Computational Physics 1998; 140:370-399.
25. Tam CKW, Webb JC. Dispersion-relation-preserving finite difference schemes for computational acoustics. Journal of Computational Physics 1993; 107:262-281.
26. Ladyzhenskaya OA. The Mathematical Theory of Viscous Incompressible Flow. Gordon and Breach: New York, 1969.
27. Sheu TWH, Chiu PH. A divergence-free-condition compensated method for incompressible Navier-Stokes equations. Computer Methods in Applied Mechanics and Engineering 2007; 196:4479-4494.
28. Leonard BP. The ULTIMATE conservative difference scheme. Computer Methods in Applied Mechanics and Engineering 1991; 88:17-74.
29. Sussman M, Smereka P, Osher S. A level set approach for computing solution to incompressible two-phase flow. Journal of Computational Physics 1994; 114:146-159.
30. Oevel W, Sofroniou W. Symplectic Runge-Kutta Schemes II: Classification of Symplectic Method, University of Paderborn, Germany, 1997.
31. Van der Pijl SP, Segal A, Vuik C, Wesseling P. A mass-conserving level-set method for modelling of multi-phase flows. International Journal for Numerical Methods in Fluids 2005; 47:339-361.
32. Zalesak ST. Fully multidimensional flux corrected transport algorithms for fluids. Journal of Computational Physics 1979; 31:335-362.
33. Ghia U, Ghia KN, Shin CT. High- Resolutions for incompressible flow using the Navier-Stokes equations and a multigrid method. Journal of Computational Physics 1982; 48:387-411.
34. Martin J, Moyce W. An experimental study of the collapse of liquid columns on a rigid horizontal plane. Philosophical Transactions 1952; 224:312-324.
35. Kelecy FJ, Pletcher RH. The development of a free surface capturing approach for multidimensional free surface flows in closed containers. Journal of Computational Physics 1997; 138:939-980.