Hostname: page-component-78c5997874-s2hrs Total loading time: 0 Render date: 2024-11-14T15:18:26.363Z Has data issue: false hasContentIssue false
  • English
  • Français

Interface Reconstruction with Split Lagrangian Advection for Two-Dimensional Interfacial Flows

Published online by Cambridge University Press:  20 December 2012

C. S. Wu  and
D. L. Young
C. S. Wu
Affiliation:
Department of Civil Engineering and Hydrotech Research Institute, National Taiwan University, Taipei, Taiwan 10617, R.O.C.
D. L. Young*
Affiliation:
Department of Civil Engineering and Hydrotech Research Institute, National Taiwan University, Taipei, Taiwan 10617, R.O.C.
*
*Corresponding author (, [email protected])
Get access

Abstract

This paper contributes to propose a 2D practical interface tracking algorithm of volume-of-fluid (VOF) method through the improved interface reconstruction, namely using both mixed Youngs centered column method (MYCCM) and the Lagrangian split advection scheme. A computationally efficiency and second-order accuracy for interface reconstruction method is presented and approximated by heuristic algorithms based on the piecewise linear interface calculation (PLIC) concept. The method can be accurately estimated by a regular structured mesh without any geometrical modifications. Besides, a linear mapping technique is implemented to improve the efficiency of numerical simulations with regard to the approximation for capturing the interface. The computational tests include widely used benchmark cases, such as the solid-body translations and rotations and the swirled single vortex of fluid body. Its performances of the improved algorithm are compared against other classical VOF advection methods. Good results are obtained by using present algorithm.

Keywords

Volume-of-fluidInterface trackingAdvectionMixed Youngs centered column methodPiecewise linear interface reconstruction
Type
Articles
Information
Journal of Mechanics , Volume 29 , Issue 2 , June 2013 , pp. 253 - 262
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2013

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

1.Chen, S., Johnson, D., Raad, P. and Fadda, D., “The Surface Marker and Micro Cell Method,” International Journal for Numerical Methods in Fluids, 25, pp. 749–778 (1997).3.0.CO;2-O>CrossRefGoogle Scholar
2.Torres, D. and Brackbill, J. U., “The Point-Set Method: Front Tracking Without Connectivity,” Journal of Computational Physics, 165, pp. 620–644 (2000).Google Scholar
3.Osher, S. and Sethian, J., “Front Propagating with Curvature-Dependent Speed: Algorithm Based on Hamilton-Jacobi Formulations,” Journal of Computational Physics, 79, pp. 12–49 (1988).Google Scholar
4.Sethian, J., Level Set Methods and Fast Marching Methods. Cambridge University Press (1995).Google Scholar
5.Gueyffier, D., Li, J., Nadim, A., Scardovelli, R. and Zaleski, S., “Volume-of-Fluid Interface Tracking with Smoothed Surface Stress Methods for Three-Dimensional Flows,” Journal of Computational Physics, 152, pp. 423–456 (1999).Google Scholar
6.Hirt, C. W. and Nichols, B. D., “Volume of Fluid (VOF) Method for the Dynamics of Free Boundaries,” Journal of Computational Physics, 39, pp. 201–225 (1981).Google Scholar
7.Aus der Wiesche, S., “The Cauchy Surface Wave Problem from Viewpoint of a VOF Method,” Computational Mechanics, 39, pp. 141–152 (2007).Google Scholar
8.Scardovelli, R. and Zaleski, S., “Note: Analytical Relations Connecting Linear Interfaces and Volume Fractions in Rectangular Grids,” Journal of Computational Physics, 164, pp. 228–237 (2000).Google Scholar
9.Sun, D. L. and Tao, W. Q., “A Coupled Volume-of-Fluid and Level Set (VOSET) Method for Computing Incompressible Two-Phase Flows,” International Journal of Heat and Mass Transfer, 53, pp. 645–655 (2010).Google Scholar
10.Mencinger, J. and Žun, I., “A PLIC-VOF Method Suited for Adaptive Moving Grids,” Journal of Computational Physics, 230, pp. 644–663 (2011).CrossRefGoogle Scholar
11.Weymouth, G. D. and Yue, D. K.-P., “Conservative Volume-of-Fluid Method for Free-Surface Simulations on Cartesian-Grids,” Journal of Computational Physics, 229, pp. 2853–2865 (2010).Google Scholar
12.Noh, W. F. and Woodward, P., SLIC (simple line interface calculation). Lecture Notes in Physics, Springer-Verlag, Berlin, pp. 330–340 (1976).Google Scholar
13.Youngs, D. L., Time-Dependent Multi-Material Flow with Large Fluid Distortion, in Numerical Method for Fluid Dynamics, edited by Morton, K.W. and Baines, M.J., Academic Press, New York (1982).Google Scholar
14.Rider, W. J. and Kothe, D. B., “Reconstructing Volume Tracking,” Journal of Computational Physics, 141, pp. 112–152 (1998).CrossRefGoogle Scholar
15.Kothe, D. B. and Rider, W. J., “A Comparison of Interface Tracking Methods,” Los Alamos Scientific Laboratory, Los Alamos, LA-UR-95-1145, New Mexico (1995).Google Scholar
16.Puckett, E. G., “A Volume-of-Fluid Interface Tracking Algorithm with Applications to Computing Shock Wave Refraction,” Proceedings of the Fourth International Symposium on Computational Fluid Dynamics, pp. 933–938 (1991).Google Scholar
17.Pilliod, J. E. and Puckett, E. G., “Second-Order Accurate Volume-of-Fluid Algorithms for Tracking Material Interfaces,” Journal of Computational Physics, 199, pp. 465–502 (2004).Google Scholar
18.Zhang, Q. and Liu, P. L.-F., “A New Interface Tracking Method: The Polygonal Area Mapping Method,” Journal of Computational Physics, 227, pp. 4063–4088 (2008).CrossRefGoogle Scholar
19.Aulisa, E., Manservisi, S., Scardovelli, R. and Zaleski, S., “Interface Reconstruction with Least-Squares Fit and Split Advection in the Three-Dimensional Cartesian Geometry,” Journal of Computational Physics, 225, pp. 2301–2319 (2007).Google Scholar
20.Scardovelli, R. and Zaleski, S., “Interface Reconstruction with Least-Square Fit and Split Eulerian-Lagrangian Advection,” International Journal for Numerical Methods in Fluids, 41, pp. 251–274 (2003).Google Scholar
21.Harvie, D. J. E. and Fletcher, D. F., “A New Volume of Fluid Advection Algorithm: The Defined Donating Region Scheme,” International Journal for Numerical Methods in Fluids, 35, pp. 151–172 (2001).3.0.CO;2-4>CrossRefGoogle Scholar
22.Ketabdri, M. J., Nobari, M. R. H. and Moradi Laraei, M., “Simulation of Waves Group Propagation and Breaking in Coastal Zone Using a Navier-Stokes Solver with an Improved VOF Free Surface Treat- ment,” Applied Ocean Research, 30, pp. 130–143 (2008).Google Scholar
23.Rudman, M., “Volume Tracking Methods for Interfacial Flow Calculations,” International Journal for Numerical Methods in Fluids, 24, pp. 671–691 (1997).3.0.CO;2-9>CrossRefGoogle Scholar
24.Harvie, D. J. E. and Fletcher, D. F., “A New Volume of Fluid Advection Algorithm: The Stream Scheme,” Journal of Computational Physics, 162, pp. 1–32 (2000).Google Scholar
25.López, J., Hernádez, J., Gómez, P. and Faura, F., “An Improved PLIC-VOF Method for Tracking Thin Fluid Structures in Incompressible Two-Phase Flows,” Journal of Computational Physics, 208, pp. 51–74 (2005).Google Scholar