A general moving mesh framework in 3D and its application for simulating the mixture of multi-phase flows

Communications in Computational Physics

Volumn 3, Issue 3, 2008, Pages 582-602

  Di, Yana ^a   Li, Ruo ^b   Tang, Tao ^c,d  

^a CHINESE ACADEMY OF SCIENCES   (China)

^b PEKING UNIVERSITY   (China)

^c HONG KONG BAPTIST UNIVERSITY   (Hong Kong)

^d BEIHANG UNIVERSITY   (China)

Author keywords

Finite element method; Moving mesh methods; Multi phase flows; Navier Stokes equations; Phase field model; Unstructured tetrahedra

Indexed keywords

EID: 41749090913     PISSN: 18152406     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (35)

1. D. M. Anderson, G. B. McFadden and A. A. Wheeler, Diffuse-interface methods in fluid mechanics, Annu. Rev. Fluid Mech., 30 (1998), 139-165.
2. E. Aulisa, S. Manservisi and R. Scardovelli, A mixed markers and volume-of-fluid method for the reconstruction and advection of interfaces in two-phase and free-boundary flows, J. Comput. Phys., 188 (2003), 611-639.
3. B. N. Azarenok and T. Tang, Second-order godunov-type scheme for reactive flow calculations on moving meshes, J. Comput. Phys., 106 (2005), 48-80.
4. G. Beckett, J. A. Mackenzie and M. L. Robertson, An r-adaptive finite element method for the solution of the two-dimensional phase-field equations, Commun. Comput. Phys., 1 (2006), 805-826.
5. J. U. Brackbill, An adaptive grid with directional control, J. Comput. Phys., 108 (1993), 38-50.
6. J. U. Brackbill and J. S. Saltzman, Adaptive zoning for singular problems in two dimensions, J. Comput. Phys., 46 (1982), 342-368.
7. A. Brandt, S. F. McCormick and J. W. Ruge, Algebraic multigrid (AMG) for sparse matrix equations, in: D. J. Evans (Ed.), Sparsity and its Applications, Cambridge University Press, Cambridge, 1984.
8. W. M. Cao, W. Z. Huang and R. D. Russell, A study of monitor functions for two dimensional adaptive mesh generation, SIAM J. Sci. Comput., 20 (1999), 1978-1994.
9. H. D. Ceniceros and T. Y. Hou, An efficient dynamically adaptive mesh for potentially singular solutions, J. Comppt. Phys., 172 (2001), 609-639.
10. F. S. de Sousa, N. Mangiavacchi, L. G. Nanato, A. Castelo, M. F. Tome, V. G. Ferreira, J. A. Cuminato and S. McKee, A front-tracking/ front-capturing method for the simulation of 3d multi-fluid flows with free surfaces, J. Comput. Phys., 198 (2004), 469-499.
11. Y. Di, R. Li, T. Tang and P. W. Zhang, Moving mesh methods for singular problems on a sphere using perturbed harmonic mappings, SIAM J. Sci. Comput., 28 (2006), 1490-1508.
12. Y. Di, R. Li, T. Tang, and P. W. Zhang, Moving mesh finite element methods for the incompressible Navier-Stokes equations, SIAM J. Sci. Comput., 26 (2005), 1036-1056.
13. Y. Di, R. Li, T. Tang and P. W. Zhang, Level set calculations for incompressible two-phase flows on a dynamically adaptive grid, J. Sci. Comput., 31(1-2) (2006), 75-98.
14. Y. Di and P. W. Zhang, Moving mesh kinetic simulation for sheared rodlike polymers with high potential intensities, Commun. Comput. Phys., 1 (2006), 859-873.
15. A. S. Dvinsky, Adaptive grid generation from harmonic maps on Riemannian manifolds, J. Comput. Phys., 95 (1991), 450-476.
16. D. Enright, R. Fedkiw, J. Ferziger and I. Mitchell, A hybrid particle level set methods for improved interface capturing, J. Comput. Phys., 183 (2002), 83-116.
17. J. L. Guermond, P. Minev and J. Shen, An overview of projection methods for incompressible flows, Comput. Method. Appl. Mech. Engrg., 1 (2006), 1-41.
18. M. Kang, R. Fedkiw and X-D. Liu, A boundary condition capturing method for multiphase incompressible flow, J. Sci. Comput., 15 (2000), 323-360.
19. R. Li, T. Tang and P.-W. Zhang, Moving mesh methods in multiple dimensions based on harmonic maps, J. Comput. Phys., 170 (2001), 562-588.
20. R. Li, T. Tang and P.-W. Zhang, A moving mesh finite element algorithm for singular problems in two and three space dimensions, J. Comput. Phys., 177 (2002), 365-393.
21. C. Liu and J. Shen, A phase field model for the mixture of two incompressible fluids and its approximation by a Fourie-spectral method, Physica D, 179 (2003), 211-228.
22. M. S. Longuet-Higgins and E. D. Cocklet, Deformation of steep surface waves on water I: A, numerical method of computation, Proc. R. Soc. Lond. A, 350 (1975), 1-25.
23. F. Losasso, R. Fedkiw and S. Osher, Spatially adaptive techniques for level set methods and incompressible flow, Comput. Fluids, 35 (2006), 995-1010.
24. S. Osher and J. A. Sethian, Fronts propagation with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations, J. Comput. Phys., 79 (1988), 12-49.
25. M. Sussman and E. G. Puckett, A coupled level set and volume-of-fluid method for computing 3d and axisymmetric incompressible two-phase flows, J. Comput. Phys., 162 (2000), 301-337.
26. M. Sussman, R Smeraka. and S. J. Osher, A level set-approach for computing solutions to incompressible two-phase flow, J. Comput. Phys., 114 (1994), 146-159.
27. H. Z. Tang, A moving mesh method for the euler flow calculations using a directional monitor function, Commun. Comput. Phys., 1 (2006), 656-676.
28. H. Z. Tang and T. Tang, Adaptive mesh methods for one- and two-dimensional hyperbolic conservation laws, SIAM J. Numer. Anal., 41 (2003), 487-515.
29. A.-K. Tomberg and B. Engquist, A finite element based level set method for multiphase flow applications, Comput. Visual. Sci., 3 (2000), 93-101.
30. S. Unverdi and G. Tryggvason, A front-tracking method for viscous, incompressible, multi-fluid flows, J. Comput. Phys., 100 (1992), 25-37.
31. A. Winslow, Numerical solution of the quasi-linear Poisson equation, J. Comput. Phys., 1 (1967), 149-172.
32. X. Yang, J. J. Feng, C. Liu and J. Shen, Numerical simulations of jet pinching-off and drop formation using an energetic variational phase-field method, J. Comput. Phys., 218 (2006), 417-428.
33. X. Yang, A. J. Lowengrub, X. Zheng and V. Cristini, An adaptive coupled level-set/volume-of-fluid interface capturing method for unstructured triangular grids, J. Comput. Phys., 217 (2006), 364-394.
34. P. Yue, J. J. Feng, C. Liu and J. Shen, A diffuse-interface method for simulating two-phase flows of complex fluids, J. Fluid Mech., 515 (2004), 293-317.
35. 2-projection, Commun. Comput. Phys., 1 (2006), 930-944.