On the elliptic mesh generation in domains containing multiple inclusions and undergoing large deformations

Journal of Computational Physics

Volumn 228, Issue 6, 2009, Pages 1980-2011

  Chatzidai, N ^a   Giannousakis, A ^a   Dimakopoulos, Y ^a   Tsamopoulos, J ^a  

^a UNIVERSITY OF PATRAS   (Greece)

Author keywords

Elliptic mesh generation; Moving boundary problems; Structured meshes

Indexed keywords

ACOUSTIC FIELDS; CONFORMAL MAPPING; DOMAIN DECOMPOSITION METHODS; FINITE ELEMENT METHOD; PROBLEM SOLVING; VISCOELASTICITY;

ARBITRARY LAGRANGIAN EULERIAN METHOD; ELLIPTIC MESH GENERATION; LARGER DEFORMATIONS; MOVING BOUNDARY PROBLEMS; MULTIPLE INCLUSIONS; NODE DISTRIBUTION; PHYSICAL DOMAIN; QUASI-ELLIPTIC; SINGULAR POINTS; STRUCTURED MESH;

MESH GENERATION;

EID: 59149104835     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2008.11.020     Document Type: Article

References (63)

1. Khamayseh A., Kuprat A., and Mastin C.W. Boundary orthogonality in elliptic grid generation. In: Thompson J.F., Soni B.K., and Weatherhill N.P. (Eds). Handbook of Grid Generation (1999), CRC Press, Boca Raton, FL
2. Saksono P.H., and Peric D. On finite element modeling of surface tension. Variational formulation and applications - part II: dynamic problems. Comput. Mech. 38 (2006) 251-263
3. Hirt C.W., and Nichols B.D. Volume of Fluid (VOF) method for the dynamics of free boundaries. J. Comput. Phys. 39 (1981) 201-225
4. Unverdi S.O., and Tryggvason G. A front-tracking method for viscous, incompressible, multi-fluid flows. J. Comput. Phys. 100 (1992) 25-37
5. Zacharioudaki M., Kouris C., Dimakopoulos Y., and Tsamopoulos J. A direct comparison between volume and surface tracking methods with a boundary-fitted coordinate transformation and third-order upwinding. J. Comput. Phys. 227 (2007) 1428-1469
6. Smith R.E. Algebraic grid generation. Appl. Math. Comput. 10-11 (1982) 137-170
7. In: Thompson J.F., Soni B.K., and Weatherhill N.P. (Eds). Handbook of Grid Generation (1999), CRC Press, Boca Raton, FL
8. Thompson J.F., Warsi Z.U.A., and Mastin W.C. Boundary-fitted coordinate systems for numerical solutions partial differential equations - a review. J. Comput. Phys. 47 (1982) 1-108
9. Ryskin G., and Leal L.G. Orthogonal mapping. J. Comput. Phys. 50 (1983) 71-100
10. Christodoulou K.N., and Scriven L.E. Discretization of free surface flows and another moving boundary problems. J. Comput. Phys. 99 (1992) 39-55
11. Tsiveriotis K., and Brown R.A. Boundary-conforming mapping applied to computations of highly deformed solidification interface. Int. J. Numer. Meth. Fluids 14 (1992) 981-1003
12. Tsiveriotis K., and Brown R.A. Solution of free-boundary problems using finite-element/Newton methods and locally refined grids: application to analysis of solidification microstructure. Int. J. Numer. Meth. Fluids 16 (1993) 827-843
13. Dimakopoulos Y., and Tsamopoulos J.A. A quasi-elliptic transformation for moving boundary problems with large anisotropic deformations. J. Comput. Phys. 192 (2003) 494-522
14. Dimakopoulos Y., and Tsamopoulos J.A. Transient displacement of a viscoplastic material by air in straight and suddenly constricted tubes. J. Non-Newton. Fluid Mech. 112 (2003) 43-75
15. Dimakopoulos Y., and Tsamopoulos J.A. Transient displacement of a Newtonian fluid by air in straight and suddenly constricted tubes. Phys. Fluids 15 7 (2003) 1973-1991
16. Dimakopoulos Y., and Tsamopoulos J.A. On the gas-penetration in straight tubes completely filled with a viscoelastic fluid. J. Non-Newton. Fluid Mech. 117 (2004) 117-139
17. Dimakopoulos Y., and Tsamopoulos J.A. Transient displacement of a Newtonian and viscoplastic liquid by air in complex tubes. J. Non-Newton. Fluid Mech. 142 (2007) 162-182
18. Foteinopoulou K., Mavrantzas V., Dimakopoulos Y., and Tsamopoulos J.A. Numerical simulation of multiple bubbles growing in a Newtonian liquid filament undergoing stretching. Phys. Fluids 18 4 (2006) 042106(24pp.)
19. Foteinopoulou K., Mavrantzas V., and Tsamopoulos J.A. Numerical simulation of bubble growth in Newtonian and viscoelastic filaments undergoing stretching. J. Non-Newton. Fluid Mech. 122 (2004) 177-200
20. Karapetsas G., and Tsamopoulos J.A. Transient squeeze flow of viscoplastic materials. J. Non-Newton. Fluid Mech. 133 (2006) 35-56
21. Tsamopoulos J., Dimakopoulos Y., Chatzidai N., Karapetsas G., and Pavlidis M. Steady bubble rise and deformation in Newtonian and viscoplastic fluids and conditions for their entrapment. J. Fluid Mech. 601 (2008) 123-164
22. Karapetsas G., and Tsamopoulos J. Steady extrusion of viscoelastic materials from an annular die. J. Non-Newton. Fluid Mech. 154 (2008) 136-152
23. Carvalho M.S., and Scriven L.E. Three-dimensional stability analysis of free surface flows: application to forward deformable roll coating. J. Comput. Phys. 151 (1999) 534-562
24. Kallinderis Y., and Kontzialis C. A priori mesh quality estimation via direct relation between truncation error and mesh distortion. J. Comput. Phys. 228 3 (2009) 881-902
25. Sackinger P.A., Schunk P.R., and Rao R.R. A Newton-Raphson pseudo-solid domain mapping technique for free and moving boundary problems: a finite element implementation. J. Comput. Phys. 125 (1996) 83-103
26. Madasu S., and Cairncross R.A. Effect of substrate flexibility on dynamic wetting: a finite element model. Comput. Meth. Appl. Mech. Eng. 192 (2003) 2671-2702
27. Thompson J.F., Warsi Z.U.A., and Mastin C.W. Numerical Grid Generation (1985), North-Holland, Amsterdam
28. Thompson J.F., Thames F.C., and Mastin C.W. Automatic numerical generation of body-fitted curvilinear coordinate system for field containing any number of arbitrary 2D bodies. J. Comput. Phys. 15 (1974) 299-319
29. Villamizar V., Rojas O., and Mabey J. Generation of curvilinear coordinates on multiply connected regions with boundary singularities. J. Comput. Phys. 223 (2007) 571-588
30. Thompson J.F. A general 3D elliptic grid generation system on a composite block structure. Comput. Meth. Appl. Mech. Eng. 64 (1987) 377-411
31. Baker T.J. Mesh generation: art or science?. Prog. Aerosp. Sci. 41 (2005) 29-63
32. Kim C. Collapse of spherical bubbles in Maxwell fluids. J. Non-Newton. Fluid Mech. 55 (1994) 37-58
33. Brujan E.A. A first order bubble dynamics in a compressible viscoelastic liquid. J. Non-Newton. Fluid Mech. 84 (1999) 83-103
34. Papanastasiou A.C., Scriven L.E., and Macosko C.W. Bubble growth and collapse in viscoelastic liquids analyzed. J. Non-Newton. Fluid Mech. 16 (1984) 53-75
35. Bousfield D.W., Keunings R., and Denn M.M. Transient deformation of an inviscid inclusion in a viscoelastic extensional flow. J. Non-Newton. Fluid Mech. 27 (1988) 205-221
36. Bjerknes V.F.K. Fields of Force (1906), Columbia University Press
37. V.F.K. Bjerknes, Die Craftfelder, Vieweg, 1909.
38. Parlitz U., Mettin R., Luther S., Akhatov I., Voss M., and Lauterborn W. Spatio-temporal dynamics of acoustic cavitation bubble clouds. Phil. Trans. R. Soc. Lond. 357 (1999) 313-334
39. Plesset M.S., and Prosperetti A. Bubble dynamics and cavitation. Annu. Rev. Fluid Mech. 9 (1977) 145-185
40. Doinikov A.A., and Zavtrak S.T. On the mutual interaction of two gas bubbles in a sound field. Phys. Fluids 7 8 (1995) 1923-1930
41. Pelekasis N.A., and Tsamopoulos J.A. Bjerknes forces between two bubbles. Part 1. Response to a step change in pressure. J. Fluid Mech. 254 (1993) 467-499
42. Pelekasis N.A., and Tsamopoulos J.A. Bjerknes forces between two bubbles. Part 2. Response to an oscillatory pressure field. J. Fluid Mech. 254 (1993) 501-527
43. Phan-Thien N., and Tanner R.I. A new constitutive equation derived from network theory. J. Non-Newton. Fluid Mech. 2 (1977) 353-365
44. Phan-Thien N., and Tanner R.I. A nonlinear network viscoelastic model. J. Rheol. 22 (1978) 259-283
45. Brown R.A., Szady M.J., Northey P.J., and Armstrong R.C. On the numerical stability of mixed finite-element methods for viscoelastic flows governed by differential constitutive equations. Theor. Comput. Fluid Dyn. 5 (1993) 77-106
46. Papanastasiou T.C., Malamataris N., and Ellwood K. A new outflow boundary condition. Int. J. Numer. Meth. Fluids 14 (1992) 587-608
47. Saltzman J., and Brackbill J. Applications and generalizations of variational methods for generating adaptive meshes. Numerical Grid Generation (1982), Elsevier, Amsterdam 865-884
48. Dvinsky A.S. Adaptive grid generation from harmonic maps on Riemannian manifold. J. Comput. Phys. 95 (1991) 450-476
49. Chung T.J. Computational Fluid Dynamics (2002), Cambridge University Press pp. 533-580
50. Szabo B., and Babuska I. Finite Element Analysis (1991), Wiley, New York
51. Brooks A.N., and Hughes T.J.R. Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations. Comput. Appl. Mech. Eng. 32 (1982) 199-259
52. Zienkiewicz O.C., and Taylor R.L. The Finite Element Method. fifth ed. (2000), Butterworth-Heinemann, Oxford
53. Codina R. Comparison of some finite element methods for solving the diffusion-convection-reaction equation. Comput. Meth. Appl. Mech. Eng. 156 (1998) 185-210
54. Gresho P.M., Lee R.L., and Sani R.L. On the time-dependent solution of the incompressible Navier-Stokes equations in two and three dimensions. In: Taylor C., and Morgan K. (Eds). Recent Advances in Numerical Methods in Fluids (1980), Pineridge Press, Swansea, UK 27-81
55. Fortin M., and Fortin A. A new approach for the FEM simulation of viscoelastic flows. J. Non-Newton. Fluid Mech. 32 (1989) 295-310
56. Cockburn B. Devising discontinuous Galerkin methods for non-linear hyperbolic conservation laws. J. Comput. Appl. Math. 128 (2001) 187-204
57. Schenk O., and Gärtner K. Solving unsymmetric sparse systems of linear equations with PARDISO. J. Future Generat. Comput. Syst. 20 3 (2004) 475-487
58. Schenk O., and Gärtner K. On fast factorization pivoting methods for symmetric indefinite systems. Electron. Trans. Numer. Anal. 23 (2006) 158-179
59. Jester W., and Kallinderis Y. Numerical study of incompressible flow around fixed cylinder pairs. J. Fluids Struct. 17 (2003) 561-577
60. Kallinderis Y., and Nakajima K. Finite element method for incompressible viscous flows with adaptive hybrid grids. AIAA J. 32 (1994) 1617-1625
61. Bird R.B., Armstrong R.C., and Hassager O. Dynamics of Polymeric Liquids (1987), John Wiley and Sons, New York
62. Miller C.A., and Scriven L.E. The oscillations of a fluid droplet immersed in another fluid. J. Fluid Mech. 32 (1968) 417-435
63. Lehoucq R.B., Sorensen D.C., and Young C. ARPACK User's Guide: Solution of Large Scale Eigenvalue Problems with Implicitly Restarted Arnoldi methods (1998), SIAM, Philadelphia, PA