Commun. Comput. Phys., 11 (2012), pp. 215-248.

A Preconditioned Implicit Free-Surface Capture Scheme for Large Density Ratio on Tetrahedral Grids

Xin Lv 1*, Qingping Zou 2, D. E. Reeve 3, Yong Zhao 4

1 International Center for Numerical Methods in Engineering (CIMNE)-Singapore, 51 Science Park Road, #04-20, The Aries Singapore Science Park II, 117586, Singapore.
2 Department of Civil and Environmental Engineering, University of Maine, Orono, Maine 04469, USA.
3 Center for Coastal Dynamics and Engineering, School of Engineering, University of Plymouth, Devon PL4 8AA, United Kingdom.
4 College of Engineering, Alfaisal University, Al Maathar Road, P.O. Box 50927, Riyadh 11533, Kingdom of Saudi Arabia.

Received 17 May 2010; Accepted (in revised version) 29 March 2011
Available online 8 September 2011


We present a three dimensional preconditioned implicit free-surface capture scheme on tetrahedral grids. The current scheme improves our recently reported method [10] in several aspects. Specifically, we modified the original eigensystem by applying a preconditioning matrix so that the new eigensystem is virtually independent of density ratio, which is typically large for practical two-phase problems. Further, we replaced the explicit multi-stage Runge-Kutta method by a fully implicit Euler integration scheme for the Navier-Stokes (NS) solver and the Volume of Fluids (VOF) equation is now solved with a second order Crank-Nicolson implicit scheme to reduce the numerical diffusion effect. The preconditioned restarted Generalized Minimal RESidual method (GMRES) is then employed to solve the resulting linear system. The validation studies show that with these modifications, the method has improved stability and accuracy when dealing with large density ratio two-phase problems.

AMS subject classifications: 65E05

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Key words: VOF, level set, free surface, unstructured finite volume method, implicit method, restarted GMRES, tetrahedral grid.

*Corresponding author.
Email: (X. Lv), (Q.-P. Zou), (D. E. Reeve), (Y. Zhao)

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