An adaptive coupled level-set/volume-of-fluid interface capturing method for unstructured triangular grids Xiaofeng Yang a , Ashley J. James a, * , John Lowengrub b , Xiaoming Zheng b , Vittorio Cristini c a Department of Aerospace Engineering and Mechanics, University of Minnesota, 107 Akerman Hall, 110 Union St SE, Minneapolis, MN 55455, USA b School of Mathematics, University of California, Irvine, USA c Biomedical Engineering, University of California, Irvine, USA Received 10 January 2005; received in revised form 4 January 2006; accepted 5 January 2006 Available online 2 March 2006 Abstract We present an adaptive coupled level-set/volume-of-fluid (ACLSVOF) method for interfacial flow simulations on unstructured triangular grids. At each time step, we evolve both the level set function and the volume fraction. The level set function is evolved by solving the level set advection equation using a discontinuous Galerkin finite element method. The volume fraction advection is performed using a Lagrangian–Eulerian method. The interface is reconstructed based on both the level set and the volume fraction information. In particular, the interface normal vector is calculated from the level set function while the line constant is determined by enforcing mass conservation based on the volume fraction. Dif- ferent from previous works, we have developed an analytic method for finding the line constant on triangular grids, which makes interface reconstruction efficient and conserves volume of fluid exactly. The level set function is finally reinitialized to the signed distance to the reconstructed interface. Since the level set function is continuous, the normal vector calcula- tion is easy and accurate compared to a classic volume-of-fluid method, while tracking the volume fraction is essential for enforcing mass conservation. The method is also coupled to a finite element based Stokes flow solver. The code validation shows that our method is second order and mass is conserved very accurately. In addition, owing to the adaptive grid algo- rithm we can resolve complex interface changes and interfaces of high curvature efficiently and accurately. Ó 2006 Elsevier Inc. All rights reserved. Keywords: VOF; Level set; Interface; Unstructured grid 1. Introduction Flows involving two or more different fluids are very common in many natural and industrial processes, for example, rain drops in the air, free surface flows in the ocean, the dispersion of two immiscible fluids into each 0021-9991/$ - see front matter Ó 2006 Elsevier Inc. All rights reserved. doi:10.1016/j.jcp.2006.01.007 * Corresponding author. Tel.: +1 612 625 6027; fax: +1 612 626 1558. E-mail address: ajames@aem.umn.edu (A.J. James). Journal of Computational Physics 217 (2006) 364–394 www.elsevier.com/locate/jcp