A moving unstructured staggered mesh method for the simulation of incompressible free-surface flows

Journal of Computational Physics

Volumn 184, Issue 1, 2003, Pages 192-214

  Perot, Blair ^a   Nallapati, Ramesh ^a  

^a UNIVERSITY OF MASSACHUSETTS   (United States)

Author keywords

Free surface; Incompressible; Navier Stokes; Staggered mesh; Unstructured

Indexed keywords

MESH GENERATION; NAVIER STOKES EQUATIONS; NUMERICAL METHODS; POISSON EQUATION;

CONSERVATION PROPERTIES; FLOW PROBLEMS; FREE SURFACES; INCOMPRESSIBLE; INCOMPRESSIBLE FREE SURFACE FLOWS; MESH DISCRETIZATIONS; MESH MOTION; NAVIER STOKES; STAGGERED MESH; UNSTRUCTURED;

INCOMPRESSIBLE FLOW;

EID: 0037280876     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0021-9991(02)00027-X     Document Type: Article

References (27)

1. Y. Tourigny, F. Hülsemann, A new moving mesh algorithm for the finite element solution of variational problems, SIAM J. Num. Anal. 35 (1998) 1416-1438.
2. T.E. Tezduyar, M. Behr, J. Liou, A new strategy for finite element computations involving moving boundaries and interfaces - the DSD/ST procedure: I. The concept and the preliminary numerical tests, Comput. Meth. Appl. Mech. Eng. 94 (1992) 339-351.
3. B. Koobus, C. Farhat, Second-order time-accurate and geometrically conservative implicit schemes for flow computations on unstructured dynamic meshes, Comput. Meth. Appl. Mech. Eng. 170 (1999) 103-129.
4. H.H. Hu, N.A. Patankar, M.Y. Zhu, Direct numerical simulations of fluid-solid systems using the arbitrary Lagrangian-Eulerian technique, J. Comput. Phys. 169 (2001) 427-462.
5. S. Li, L. Petzold, Moving mesh methods with upwinding schemes for time-dependent PDEs, J. Comp. Phys. 131 (1997) 368-377.
6. A. Harten, J.M. Hyman, A self-adjusting grid for the computation of weak solutions of hyperbolic conservation laws, J. Comput. Phys. 50 (1983) 235.
7. F.H. Harlow, J.E. Welch, Numerical calculations of time dependent viscous incompressible flow of fluid with a free surface, Phys. Fluids 8 (1965) 2182.
8. R.A. Nicolaides, The covolume approach to computing incompressible flows, in: M.Y. Hussaini, A. Kumar, M.D. Salas (Eds.), Algorithmic Trends in Computational Fluid Dynamics, Springer, Berlin, 1993, pp. 295-333.
9. R.A. Nicolaides, Direct discretization of planar div-curl problems, ICASE Report 89-76, 1989.
10. R.A. Nicolaides, The covolume approach to computing incompressible flow, in: M.D. Gunzburger, R.A. Nicolaides (Eds.), Incompressible Computational Fluid Dynamics, Cambridge University Press, Cambridge, 1993, pp. 234-295.
11. R.A. Nicolaides, X. Wu, Covolume solutions of three-dimensional div-curl equations, ICASE Report 95-4, 1995.
12. C.A. Hall, J.S. Peterson, T.A. Porsching, F.R. Sledge, The dual variable method for finite element discretizations of Navier/Stokes equations, Int. J. Num. Meth. Eng. 21 (1985) 883-898.
13. J.C. Cavendish, C.A. Hall, T.A. Porsching, A complementary volume approach for modelling three-dimensional Navier-Stokes equations using dual Delaunay/Voronoi tessellations, Int. J. Num. Meth. Heat Fluid Flow 4 (1994) 329-345.
14. J.B. Perot, Conservation properties of unstructured staggered mesh schemes, J. Comput. Phys. 159 (2000) 58-89.
15. X. Zhang, D. Schmidt, B. Perot, Accuracy and conservation properties of a three-dimensional unstructured staggered mesh scheme for fluid dynamics, J. Comput. Phys. 175 (2002) 764-791.
16. R. Nallapati, J.B. Perot, Numerical simulation of free surface flows using a moving mesh, in: Proceeedings of the 2000 American Society of Mechanical Engineers, Fluids Engineering Summer Conference, 2000.
17. J.B. Perot, X. Zhang, Reformulation of the unstructured staggered mesh method as a classic finite volume method, in: Finite Volumes for Complex Applications, vol. II, Hermes Science Publications, 1999, pp. 263-270.
18. W. Chang, F. Giraldo, J.B. Perot, Analysis of an exact fractional step method, J. Comput. Phys. 180 (2002) 183-199.
19. J.C. Strikwerda, Y.S. Lee, The accuracy of the fractional step method, SIAM J. Num. Anal. 37 (1999) 37-47.
20. J.B. Perot, An analysis of the fractional step method, J. Comput. Phys. 108 (1993) 51-58.
21. W. Huang, R.D. Russel, Analysis of moving mesh partial differential equations with spatial smoothing, SIAM J. Num. Anal. 34 (1997) 1106-1126.
22. W.G. Habashi, J. Dompierre, Y. Bourgault, D. Ait-Ali-Yahia, M. Fortin, M.-G. Vallet, Anisotropic mesh adaptation: towards user-independent, mesh-independent and solver-independent CFD solutions: Part I: General principles, Int. J. Num. Meth. Fluids 32 (6) (2000) 725-744.
23. B. Joe, Three-dimensional triangulations from local transformations, SIAM J. Sci. Statist. Comput. (1989) 718-741.
24. R. Nallapati, Numerical simulation of free-surface flows using a moving unstructured staggered grid method, Masters Thesis, University of Massachussets, Amherst, 2001.
25. F. Harlow, A. Amsden, Fluid Dynamics, an Introductory Text, Los Alamos Scientific Laboratory, LA-4700, 1980.
26. L.D. Landau, E.M. Lifshitz, Fluid Mechanics, Pergamon Press, Oxford, 1959.
27. M. Dai, H. Wang, J.B. Perot, D.P. Schmidt, Direct Interface Tracking of Droplets, Atomization and Sprays, (accepted March) 2002 (in press).