Abstract
By coupling the standard and the conservative level set methods, an improved conservative level set method is proposed to capture the free surface smoothly with excellent mass conservation properties. The improvement lies in the fact that the surface normal is computed from a signed distance function instead of the Heaviside function. Comparing with the conservative level set method, the inevitable numerical discretization errors to point the surface normal in arbitrary directions could be eliminated, and the instability of the numerical solution could be improved efficiently. The advantage is clear in the straightforward combination of the standard level set and the conservative level set and a little effort is taken in coding compared with other coupled methods. The present method is validated with several well-known benchmark problems, including the 2-D Zalesak’s disk rotating, the 3-D sphere stretching in deformation vortex and the dam break flow simulation. The results are shown to be in good agreement with the published experimental data and numerical results.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
CIORTAN C., WANDERLEY J. B. V. and GUEDE-SSOARES C. Free surface flow around a ship model using an interface-capturing method[J]. Ocean Engi neering, 2012, 44(4): 57–67.
RAINALD L., CHI Y. and EUGENIO O. Simulation of flows with violent free surface motion and moving objects using unstructured grids[J]. International Journal for Numerical Methods in Fluids, 2007, 53(8): 1315–1338.
YU G., AVITAL E. J., and WILLIAMS J. J. R. Large eddy simulation of flow past free surface piercing circular cylinders[J]. Journal of Fluids Engineering, 2008, 130(10): 101304.
TONY W. H. S., YU C. H. and CHIU P. H. Development of level set method with good area preservation to predict interface in two-phase flows[J]. International Journal for Numerical Methods in Fluids, 2011, 67(1): 109–134.
Van Der PIJ S. P., SEGAL A., and VUIK C. et al. A mass-conserving level-set method for modelling of multi-phase flows[J]. International Journal For Numerical Methods in Fluids, 2005, 47(4): 339–361.
DOUGLAS E., FRANK L. and RONALD F. A fast and accurate semi-Lagrangian particle level set me-thod[J]. Computers and Structures, 2005, 83(6): 479–490.
KOH C. G., GAO M. and LUO C. A new particle method for simulation of incompressible free surface flow problems[J]. International Journal for Numerical Methods in Engineering, 2012, 89(12): 1582–1604.
SUSSMAN M. A second order coupled level set and volume-of-fluid method for computing growth and collapse of vapor bubbles[J]. Journal of Computatio-nal Physics, 2003, 187(1): 110–136.
ELIN O., GUNILLA K. A conservative level set method for two phase flow[J]. Journal of Computational Physics, 2005, 210(1): 225–246.
ELIN O., GUNILLA K. and SARA Z. A conservative level set method for two phase flow Ii[J]. Journal of Computational Physics, 2007, 225(1): 785–807.
BARTO P. T., OBADIA B. and DRIKAKIS D. A conservative level-set based method for compressible solid/fluid problems on fixed grids[J]. Journal of Computational Physics, 2011, 230(21): 7867–7890.
OWKES M., DESJARDINS O. A discontinuous Galerkin conservative level set scheme for interface capturing in multiphase flows[J]. Journal of Computational Physics, 2013, 249(1): 275–302.
KEES C. E., AKKERMAN I. and FARTHING M. W. et al. A conservative level set method suitable for variable-order approximations and unstructured meshes[J]. Journal of Computational Physics, 2011, 230(12): 4536–4558.
OLIVIER D., VINCENT M. and HEINZ P. An accurate conservative level set/ghost fluid method for simulating turbulent atomization[J]. Journal of Computational Physics, 2008, 227(18): 8395–8416.
RENATO N. E., and ALVARO L. G. A. C. Stabilized edge-based finite element simulation of free-surface flows[J]. International Journal for Numerical Methods in Fluids, 2007, 54(6–8): 965–993.
CRUCHAGA M. A., CELENTANO D. J. and TEZDU-YAR T. E. Moving-interface computations with the edge-tracked interface locator technique (ETILT)[J]. International Journal for Numerical Methods in Fluids, 2005, 47(6–7): 451–469.
LOHNER R., YANG C. and ONATE E. On the simulation of flows with violent free-surface motion[J]. Computer Methods in Applied Mechanics and Engineering, 2006, 195(41–43): 5597–5620.
ELIAS R., COUTINHO A. Stabilized edge-based finite element simulation of free-surface flows[J]. International Journal of Numerical Methods in Fluids, 2007, 54(6–8): 965–993.
LV X., ZOU Q. P. and ZHAO Y. et al. A novel coupled level set and volume of fluid method for sharp interface capturing on 3D tetrahedral grids[J]. Journal of Computational Physics, 2010, 229(7): 2573–2604.
WEN X. Y. Wet/dry areas method for interfacial (free surface) flow[J]. International Journal for Numerical Methods in Fluids, 2013, 71(3): 316–338.
Author information
Authors and Affiliations
Corresponding author
Additional information
Project supported by the National Natural Science Foundation of China (Grant No. 51279050), the National High Technology Research and Development Program of China (863 Program, Grant No. 2012Bak10b04) and the Non-profit Industry Financial Program of Ministry of Water Resources of China (Grant No. 201301058)
Biography: Zhao Lan-hao (1980-), Male, Ph. D., Professor
Rights and permissions
About this article
Cite this article
Zhao, Lh., Mao, J., Liu, Xq. et al. Improved conservative level set method for free surface flow simulation. J Hydrodyn 26, 316–325 (2014). https://doi.org/10.1016/S1001-6058(14)60035-4
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1016/S1001-6058(14)60035-4