Adaptive VOF with curvature-based refinement

International Journal for Numerical Methods in Fluids

Volumn 55, Issue 7, 2007, Pages 693-712

  Malik, Mayank ^a,b   Fan, Eric Sheung Chi ^a   Bussmann, Markus ^a  

^a UNIVERSITY OF TORONTO   (Canada)

^b The University of Texas at Austin   (United States)

Author keywords

Adaptive; Curvature; Height function; VOF; Volume tracking

Indexed keywords

ADVECTION; ERRORS; FLOW PATTERNS; FUNCTIONS; INTERFACES (MATERIALS);

CURVATURE-BASED REFINEMENT; HEIGHT FUNCTION; VOLUME TRACKING; VOLUME-OF-FLUID (VOF);

NUMERICAL METHODS;

ADVECTION; ERRORS; FLOW PATTERNS; FUNCTIONS; INTERFACES (MATERIALS); NUMERICAL METHODS;

EID: 35448970183     PISSN: 02712091     EISSN: 10970363     Source Type: Journal    
DOI: 10.1002/fld.1490     Document Type: Article

References (25)

1. Devals C, Heniche M, Bertrand F, Hayes RE, Tanguy PA. A finite element strategy for the solution of interface tracking problems. International Journal for Numerical Methods in Fluids 2005; 49:1305-1327.
2. Ginzburg I, Wittum G. Two-phase flows on interface refined grids modeled with VOF, staggered finite volumes, and spline interpolants. Journal of Computational Physics 2001; 166:302-335.
3. Greaves D. A quadtree adaptive method for simulating fluid flows with moving interfaces. Journal of Computational Physics 2004; 194:35-56.
4. Greaves D. Simulation of interface and free surface flows in a viscous fluid using adapting quadtree grids. International Journal for Numerical Methods in Fluids 2004; 44:1093-1117. DOI: 10.1002/ fld.687
5. Greaves DM. Simulation of viscous water column collapse using adapting hierarchical grids. International Journal for Numerical Methods in Fluids 2006; 50:693-711. DOI: 10.1002/fld.1073
6. Hay A, Visonneau M. Computation of free-surface flows with local mesh adaptation. International Journal for Numerical Methods in Fluids 2005; 49:785-816. DOI: 10.1002/fld.1042
7. Jeong JH, Yang DY Finite element analysis of transient fluid flow with free surface using VOF (volume-of-fluid) method and adaptive grid. International Journal for Numerical Methods in Fluids 1998; 26:1127-1154.
8. Jeong JH, Yang DY. Three-dimensional finite element analysis of transient fluid flow with free-surface using marker surface method and adaptive grid refinement. International Journal for Numerical Methods in Fluids 1999; 29:657-684.
9. Kohno H, Tanahashi T. Numerical analysis of moving interfaces using a level set method coupled with adaptive mesh refinement. International Journal for Numerical Methods in Fluids 2004; 45:921-944. DOI: 10.1002/fld.715
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 2003; 187:110-136.
11. Theodorakakos A, Bergeles G. Simulation of sharp gas-liquid interface using VOF method and adaptive grid local refinement around the interface. International Journal for Numerical Methods in Fluids 2004; 45:421-439. DOI: 10.1002/fld.706
12. Wang JP, Borthwick AGL, Taylor RE. Finite-volume-type VOF method on dynamically adaptive quadtree grids. International Journal for Numerical Methods in Fluids 2004; 45:485-508. DOI: 10.1002/ fld.712
13. Losasso F, Fedkiw R, Osher S. Spatially adaptive techniques for level set methods and incompressible flow. Computers and Fluids 2006; 35:995-1010.
14. Bussmann M, Chandra S, Mostaghimi J. Modeling the splash of a droplet impacting a solid surface. Physics of Fluids 2000; 12:3121-3132.
15. Gueyffier D, Zaleski S. Formation de digitations lors de l'impact d'une goutte sur un film liquide. Comptes Rendus de l'Académie des Sciences - Série IIb: Mécanique, Physique, Chimie, Astronomie 1998; 326:839-844.
16. Rieber M, Frohn A. A numerical study on the mechanism of splashing. International Journal of Heat and Fluid Flow 1999; 20:455-461.
17. Dai M, Schmidt DP. Adaptive tetrahedral meshing in free-surface flow. Journal of Computational Physics 2005; 208:228-252.
18. Sussman M, Almgren AS, Bell JB, Colella P, Howell LH, Welcome ML. An adaptive level set approach for incompressible two-phase flows. Journal of Computational Physics 1999; 148:81-124.
19. Löhner R, Yang C, Oñate E. Simulation of flows with violent free surface motion and moving objects using unstructured grids. International Journal for Numerical Methods in Fluids 2007; 53:1315-1338. DOI: 10.1002/fld.1244
20. Youngs DL. Time-dependent multi-material flow with large fluid distortion. In Numerical Methods for Fluid Dynamics, Morton KW, Baines MJ (eds). Academic Press: New York, 1982; 273-285.
21. Pilliod Jr. JE, Puckett EG. Second-order accurate volume-of-fluid algorithms for tracking material interfaces. Journal of Computational Physics 2004; 199:465-502.
22. Samet H. The Design and Analysis of Spatial Data Structures. Addison-Wesley: Reading, MA, 1990.
23. Cummins SJ, Francois MM, Kothe DB. Estimating curvature from volume fractions. Computers and Structures 2005; 83:425-434.
24. Francois MM, Cummins SJ, Dendy ED, Kothe DB, Sicilian JM, Williams MW. A balanced-force algorithm for continuous and sharp interfacial surface tension models within a volume tracking framework. Journal of Computational Physics 2006; 213:141-173.
25. Renardy Y, Renardy M. PROST: a parabolic reconstruction of surface tension for the volume-of-fluid method. Journal of Computational Physics 2002; 183:400-421.