Transient adaptivity applied to two-phase incompressible flows

Journal of Computational Physics

Volumn 227, Issue 3, 2008, Pages 1923-1942

  Compère, Gaëtan ^a,b   Marchandise, Emilie ^a,b   Remacle, Jean François ^a  

^a UNIVERSITÉ CATHOLIQUE DE LOUVAIN   (Belgium)

^b FNRS   (Belgium)

Author keywords

Adaptivity; Anisotropic; Finite elements; Level set; Two phase

Indexed keywords

ANISOTROPY; MESH GENERATION; NUMERICAL METHODS;

ADAPTATION PROCESS; ADAPTIVITY; ANISOTROPIC; FINITE ELEMENT; FLOW SOLVER; LEVEL SET; LEVEL-SET FUNCTION; TWO PHASE; TWO PHASES FLOW; UNSTRUCTURED TETRAHEDRAL MESHES;

TWO PHASE FLOW;

EID: 37249000781     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2007.10.002     Document Type: Article

References (63)

1. Sussman M., Almgren S., Bell B., Colella P., Howell L., and Welcome M. An adaptive level set approach for incompressible two-phase flows. Journal of Computational Physics 148 (1999) 81-124
2. Y. Andrillon, Simulation d'ecoulements a surface libre par une methode de capture d'interface en formulation totalement couplee, Ph.D. thesis, Ecole centrale de Nantes et Universite de Nantes, 2004.
3. Marchandise E., Remacle J.-F., and Chevaugeon N. A quadrature-free discontinuous Galerkin method for the level set equation. Journal of Computational Physics 212 (2006) 338-357
4. Marchandise E., and Remacle J.-F. A stabilized finite element method using a discontinuous level set approach for solving two phase incompressible flows. Journal of Computational Physics 219 (2006) 780-800
5. Marchandise E., Geuzaine P., Chevaugeon N., and Remacle J.-F. A stabilized finite element method using a discontinuous level set approach for the computation of bubble dynamics. Journal of Computational Physics 225 (2007) 949-974
6. Osher S., and Sethian J.A. Fronts propagating with curvature dependent speed: algorithms based on Hamilton-Jacobi formulations. Journal of Computational Physics 79 (1988) 12-49
7. Sussman M., and Fatemi E. An efficient interface preserving level set redistancing algorithm and its application to interfacial incompressible fluid flow. SIAM Journal on Scientific Computing 20 (1999) 1165-1191
8. Hirt C., and Nichols B. Volume-of-fluid method (VOF) for the dynamics of free boundaries. Journal of Computational Physics 39 (1981) 201-225
9. Pilliot J., and Puckett E. Second order accurate volume-of-fluid algorithms for tracking material interfaces. Journal of Computational Physics 199 (2004) 465-502
10. Sussman M. A second order coupled level set and volume-of-fluid method for computing growth and collapse of vapor bubbles. Journal of Computational Physics 187 (2003) 110-136
11. Hirt C., Amsden A., and Cook J. An Arbitrary Lagrangian-Eulerian computing method for all flow speeds. Journal of Computational Physics 14 (1974) 227-253
12. Hughes T., Liu W., and Zimmermann T. Lagrangian-Eulerian finite element formulation for incompressible viscous flows. Computer Methods in Applied Mechanics and Engineering 29 (1981) 239-349
13. Donea J. Arbitrary Lagrangian-Eulerian finite element methods. Computational Methods for Transient Analysis 1 (1983) 473-516
14. Dettmer W., Saksono P., and Peric D. On a finite element formulation for incompressible Newtonian fluid flows on moving domains in the presence of surface tension. Computer Methods in Applied Mechanics and Engineering 19 (2003) 659-668
15. Harlow F., and Welch J. Volume tracking methods for interfacial flow calculations. Physics of Fluids 8 (1965) 21-82
16. Sussman M., Smereka P., and Osher S. A level set approach for computing solutions to incompressible two-phase flow. Journal of Computational Physics 114 (1994) 146-159
17. Sussman M., Fatemi E., Smereka P., and Osher S. An improved level set method for incompressible two-fluid flows. Computers and Fluids 27 (1998) 663-680
18. Chessa J., and Belytschko T. An extended finite element method for two-phase fluids. Journal of Applied Mechanics (Transactions of the ASME) 70 (2003) 10-17
19. Chessa J., and Belytschko T. An enriched finite element method and level sets for axisymmetric two-phase flow with surface tension. International Journal for Numerical Methods in Engineering 58 (2003) 2041-2064
20. Norman C., and Miksis M. Non-linear dynamics of thin films and fluid interfaces. Physica D: Nonlinear Phenomena 209 (2005) 191-204
21. Nagrath S., Jansen K., and Lahey R. Computation of incompressible bubble dynamics with a stabilized finite element level set method. Computer Methods in Applied Mechanics and Engineering 194 42-44 (2005) 4565-4587
22. Berger M., and Oliger J. Adaptive mesh refinement for hyperbolic partial differential equations. Journal of Computational Physics 53 (1984) 484-512
23. Berger M., and Colella P. Local adaptive mesh refinement for shock hydrodynamics. Journal of Computational Physics 82 (1989) 64-84
24. Pember R., Bell J., Colella P., Crutchfield W., and Welcome M. An adaptive cartesian grid method for unsteady compressible flow in irregular regions. Journal of Computational Physics 120 (1995) 278-304
25. Martin D., and Colella P. A cell-centered adaptive projection method for the incompressible Euler equations. Journal of Computational Physics 163 (2000) 271-312
26. Roma A., Peskin C., and Berger M. An adaptive version of the immersed boundary method. Journal of Computational Physics 153 (1999) 509-534
27. Sussman M., and parallelized A. adaptive algorithm for multiphase flows in general geometries. Computers and Structures 83 (2005) 435-444
28. Popinet S. Gerris: a tree-based adaptive solver for the incompressible Euler equations in complex geometries. Journal of Computational Physics 190 (2003) 572-600
29. Losasso F., Gibou F., and Fedkiw R. Simulating water and smoke with an octree data structure. ACM Transactions on Graphics (SIGGRAPH Proc) 23 (2004) 457-462
30. Greaves D. A quadtree adaptive method for simulating fluid flows with moving interfaces. Journal of Computational Physics 194 (2004) 35-56
31. Cristini V., Blawzdziewicz J., and Loewenberg M. An adaptive mesh algorithm for evolving surfaces: simulations of drop breakup and coalescence. Journal of Computational Physics 168 (2001) 445-463
32. Yang X., James A., Lowengrub J., Zheng X., and Cristini V. An adaptive coupled level-set/volume-of-fluid interface capturing method for unstructured triangular grids. Journal of Computational Physics 217 (2006) 364-394
33. Anderson A., Zheng X., and Cristini V. Adaptive unstructured volume remeshing part i: The method. Journal of Computational Physics 208 (2005) 616-625
34. Losasso F., Fedkiw R., and Osher S. Spatially adaptive techniques for level set methods and incompressible flows. Computers and Fluids 35 (2006) 995-1010
35. Remacle J.-F., Li X., Shephard M., and Flaherty J. Anisotropic adaptive simulation of transient flows using Discontinuous Galerkin methods. International Journal for Numerical Methods in Engineering 62 (2004) 899-923
36. Remacle J.-F., Soares Frazao S., Li X., and Shephard M. Adaptive discontinuous Galerkin method for the shallow water equations. International Journal for Numerical Methods in Fluids 52 (2006) 903-923
37. Babuska I. The finite element method with Lagrangian multipliers. Numerische Mathematik 20 (1971) 179-192
38. T. Barth, Aspects of Unstructured Grids and Finite-Volume Solvers for the Euler and Navier-Stokes Equations, Special Course on Unstructured Grid Methods for Advection Dominated Flows, AGARD R-787, 1992 (Chapter 4).
39. Selmin V., and Formaggia L. Unified construction of finite element and finite volume discretizations for compressible flows. International Journal for Numerical Methods in Fluids 39 (1996) 1-32
40. Geuzaine P. Newton-Krylov strategy for compressible turbulent flows on unstructured meshes. AIAA Journal 39 (2001) 528-531
41. Cai X., Farhat C., and Sarkis M. A minimum overlap restricted additive Schwarz preconditioner and applications in 3D flow simulations. Contemporary Mathematics 218 (1998) 478-484
42. Fedkiw R., Aslam T., Merriman B., and Osher S. A non-oscillatory Eulerian approach to interfaces in multimaterial flows (the ghost fluid method). Journal of Computational Physics 152 (1999) 457-492
43. Brackbill J., Kothe C., and Zemach D. A continuum method for modeling surface tension. Journal of Computational Physics 2 (1992) 335-354
44. A. Smoliansky, Numerical modeling of two-fluid interfacial flows, Ph.D. thesis, University of Jyvaskyla, Finland, 2001.
45. A.-K. Tornberg, Interface tracking methods with applications to multiphase flows, Ph.D. thesis, Royal Institute of Technology (KTH), Finland, 2000.
46. Almeida R., Feijoo P., Galeao A., Padra C., and Silva R. Adaptive finite element computational fluid dynamics using an anisotropic error estimator. Computer Methods in Applied Mechanics and Engineering 182 3-4 (2002) 379-400
47. Borouchaki H., George P.L., Hecht F., Laug P., and Saltel E. Delaunay mesh generation governed by metric specifications - part i: Algorithms and part ii: Applications. Finite Elements in Analysis and Design 25 (1997) 61-83 85-109
48. Saramito P., and Roquet N. An adaptive finite element method for viscoplastic fluid flow in pipes. International Journal for Numerical Methods in Engineering 190 (2001) 5391-5412
49. Alauzet F., George P.L., Mohammadi B., Frey P., and Borouchaki H. Transient fixed point-based unstructured mesh adaptation. International Journal for Numerical Methods in Fluids 23 (2003) 729-745
50. X. Li, Mesh modification procedures for general 3-D non-manifold domains, Ph.D. thesis, Rensselear Polytechnic Institute, 2003.
51. Dobrzynski C., Frey P.J., Mohammadi B., and Pironneau O. Fast and accurate simulations of air-cooled structures. Computer Methods in Applied Mechanics and Engineering 195 (2006) 3168-3180
52. Bernard P.-E., Chevaugeon N., Legat V., Deleersnijder E., and Remacle J.-F. High-order h-adaptative discontinuous Galerkin methods for ocean modelling. Ocean Dynamics 57 (2007) 109-121
53. Li X., Shephard M., and Beall M. 3D anisotropic mesh adaptation by mesh modification. Computer Methods in Applied Mechanics and Engineering 194 (2005) 4915-4950
54. Mount M., Arya N., Netanyahu R., and Silverman R. An optimal algorithm for Approximate Nearest Neighbor searching. Journal of the ACM 45 (1998) 891-923
55. ANN library. URL http://www.cs.umd.edu/~mount/ANN/.
56. Zheng X., Lowengrub J., Anderson A., and Cristini V. Adaptive unstructured volume remeshing ii: Application to two- and three-dimensional level-set simulations of multiphase flow. Journal of Computational Physics 208 (2005) 626-650
57. Popinet S., and Zaleski S. A front-tracking algorithm for accurate representation of surface tension. International Journal for Numerical Methods in Fluids 30 (1999) 775-793
58. Francois M., Cummins S., Dendy E., Kothe D., Sicilian J., and Williams M. A balanced-force algorithm for continuous and sharp interfacial surface tension models within a volume tracking framework. Journal of Computational Physics 213 (2006) 141-173
59. Williams M., Kothe D., and Puckett E. Convergence and accuracy of continuum surface tension models. In: Shyy W., and Narayanan R. (Eds). Fluid Dynamics at Interface (1999), Cambridge University Press, Cambridge 294-305
60. Quecedo M., Pastor M., and Herreros M. An experimental study of the collapse of liquid columns on a rigid horizontal plane. Philosophical Transactions A 244 (1952) 312-324
61. Sussman M., and Puckett E. A coupled level set and volume-of-fluid method for computing 3D and axisymmetric incompressible two-phase flows. Journal of Computational Physics 162 (2000) 301-337
62. de Sousa F., Mangiavacchi N., Nonato L., Castel A., Tome M., Ferreira V., Cuminato J., and McKee S. A front-tracking/front-capturing method for the simulation of 3D multi-fluid flows with free surfaces. Journal of Computational Physics 198 (2004) 469-499
63. Narayanan N.K.S., and Goossens H. Coalescence of two bubbles rising in line at low reynolds number. Chemical Engineering Science 29 (1974) 2071-2082