A second-order accurate material-order-independent interface reconstruction technique for multi-material flow simulations Samuel P. Schofield a, * , Rao V. Garimella a , Marianne M. Francois b , Raphaël Loubère c a Mathematical Modeling and Analysis (T-7), Los Alamos National Laboratory, Los Alamos, NM 87545, United States b Computational Physics and Methods (CCS-2), Los Alamos National Laboratory, Los Alamos, NM 87545, United States c Mathematical Institute of Toulouse, CNRS, University of Toulouse, France article info Article history: Received 17 January 2008 Received in revised form 18 September 2008 Accepted 29 September 2008 Available online 11 October 2008 Keywords: Volume-of-fluid Interface reconstruction Multi-material flow Material-order independence Linear reconstruction Centroids Power diagrams abstract A new, second-order accurate, volume conservative, material-order-independent interface reconstruction method for multi-material flow simulations is presented. First, materials are located in multi-material computational cells using a piecewise linear reconstruction of the volume fraction function. These material locator points are then used as generators to reconstruct the interface with a weighted Voronoi diagram that matches the volume fractions. The interfaces are then improved by minimizing an objective function that smoothes interface normals while enforcing convexity and volume constraints for the pure material subcells. Convergence tests are shown demonstrating second-order accuracy. Sta- tic and dynamic examples are shown illustrating the superior performance of the method over existing material-order-dependent methods. Ó 2008 Elsevier Inc. All rights reserved. 1. Introduction Multi-material and multi-phase flows occur in a variety of natural phenomena and industrial processes. To accurately model such flows, it is essential to effectively capture and manage material interfaces. Due to their ability to strictly conserve mass, volume-of-fluid (VOF) methods using interface reconstruction are widely used in such simulations [1–4]. Originally developed by Hirt and Nichols [5], VOF methods do not explicitly track interfaces but rather track the volume of each mate- rial. When required, the interface position is computed using the volume fraction data. In a flow simulation, the volume frac- tions are updated by determining the flux of each material into or out of a computational cell although in multi-material compressible simulations, volume fractions may also be modified by mixture models like pressure equilibration [1]. Contem- porary schemes use the reconstructed interface to obtain a better approximation to the material fluxes. Poor interface recon- struction directly affects material fluxes and can result in material being transported to the wrong locations and unphysical fragmentation of material. Early VOF methods used a straight line aligned with a coordinate axis to partition the cell according to the material vol- ume fractions [6]. Youngs [7,8] extended the method to permit the material interface to have an arbitrary orientation within the cell. Such methods, that allow a generally oriented interface within the cell, are referred to as piecewise linear interface calculation (PLIC) methods [3]. In Youngs’ method, the outward normal of the interface separating a material from the rest of 0021-9991/$ - see front matter Ó 2008 Elsevier Inc. All rights reserved. doi:10.1016/j.jcp.2008.09.023 * Corresponding author. Tel.: +1 505 606 1484; fax: +1 505 665 5757. E-mail addresses: sams@lanl.gov (S.P. Schofield), rao@lanl.gov (R.V. Garimella), mmfran@lanl.gov (M.M. Francois), loubere@mip.ups-tlse.fr (R. Loubère). Journal of Computational Physics 228 (2009) 731–745 Contents lists available at ScienceDirect Journal of Computational Physics journal homepage: www.elsevier.com/locate/jcp