A three-dimensional volume-of-fluid method for reconstructing and advecting three-material interfaces forming contact lines

We introduce a piecewise-linear, volume-of-fluid method for reconstructing and advecting three-dimensional interfaces and contact lines formed by three materials. The new method employs a set of geometric constructs that can be used in conjunction with any volume-tracking scheme. In this work, we used the mass-conserving scheme of Youngs to handle two-material cells, perform interface reconstruction in three-material cells, and resolve the contact line. The only information required by the method is the available volume fraction field. Although the proposed method is order dependent and requires a priori information on material ordering, it is suitable for typical contact line applications, where the material representing the contact surface is always known. Following the reconstruction of the contact surface, to compute the interface orientation in a three-material cell, the proposed method minimizes an error function that is based on volume fraction distribution around that cell. As an option, the minimization procedure also allows the user to impose a contact angle. Performance of the proposed method is assessed via both static and advection test cases. The tests show that the new method preserves the accuracy and mass-conserving property of the Youngs method in volume-tracking three materials.

[1]  Hyung Taek Ahn,et al.  Multi-material interface reconstruction on generalized polyhedral meshes , 2007, J. Comput. Phys..

[2]  M. Sussman.  A second order coupled level set and volume-of-fluid method for computing growth and collapse of vapor bubbles , 2003 .

[3]  S. Cummins,et al.  Estimating curvature from volume fractions , 2005 .

[4]  Markus Bussmann,et al.  Height functions for applying contact angles to 3D VOF simulations , 2009 .

[5]  Jérôme Breil,et al.  A 2D unstructured multi-material Cell-Centered Arbitrary Lagrangian―Eulerian (CCALE) scheme using MOF interface reconstruction , 2011 .

[6]  M. Raessi,et al.  Computational simulation of the interactions between moving rigid bodies and incompressible two-fluid flows , 2014 .

[7]  Roland Glowinski,et al.  A numerical method for interface reconstruction of triple points within a volume tracking algorithm , 2008, Math. Comput. Model..

[8]  W. Rider,et al.  Reconstructing Volume Tracking , 1998 .

[9]  Kenneth I. Joy,et al.  Discrete Multi‐Material Interface Reconstruction for Volume Fraction Data , 2008, Comput. Graph. Forum.

[10]  G. Son.  A LEVEL SET METHOD FOR INCOMPRESSIBLE TWO-FLUID FLOWS WITH IMMERSED SOLID BOUNDARIES , 2005 .

[11]  L YoungsD,et al.  Time-dependent multi-material flow with large fluid distortion. , 1982 .

[12]  Shashank Chaturvedi,et al.  Volume-of-fluid algorithm with different modified dynamic material ordering methods and their comparisons , 2010, J. Comput. Phys..

[13]  J. Ghidaglia,et al.  Dealing with more than two materials in the FVCF–ENIP method , 2013 .

[14]  S. Jakirlic,et al.  Dynamic contact angle of spreading droplets: Experiments and simulations , 2005 .

[15]  Jean-Michel Ghidaglia,et al.  A totally Eulerian finite volume solver for multi-material fluid flows , 2009, 1010.4208.

[16]  Henry N. Christiansen,et al.  A polyhedron clipping and capping algorithm and a display system for three dimensional finite element models , 1975, COMG.

[17]  E. Puckett,et al.  Second-Order Accurate Volume-of-Fluid Algorithms for Tracking Material Interfaces , 2013 .

[18]  Mehdi Raessi,et al.  Advecting normal vectors: A new method for calculating interface normals and curvatures when modeling two-phase flows , 2007, J. Comput. Phys..

[19]  William H. Press,et al.  The Art of Scientific Computing Second Edition , 1998 .

[20]  Mikhail J. Shashkov,et al.  Conservative multi-material remap for staggered multi-material Arbitrary Lagrangian-Eulerian methods , 2014, J. Comput. Phys..

[21]  J. Kuipers.  Quaternions and Rotation Sequences , 1998 .

[22]  David J. Benson,et al.  Volume of fluid interface reconstruction methods for multi - material problems , 2002 .

[23]  J. Sethian,et al.  The Voronoi Implicit Interface Method for computing multiphase physics , 2011, Proceedings of the National Academy of Sciences.

[24]  S. Chandra,et al.  On a three-dimensional volume tracking model of droplet impact , 1999 .

[25]  Ken Shoemake,et al.  Animating rotation with quaternion curves , 1985, SIGGRAPH.

[26]  David J. Benson,et al.  Eulerian finite element methods for the micromechanics of heterogeneous materials: Dynamic prioritization of material interfaces , 1998 .

[27]  Daniel Sunday.  Fast Polygon Area and Newell Normal Computation , 2002, J. Graphics, GPU, & Game Tools.

[28]  P. Colella,et al.  Non-convex profile evolution in two dimensions using volume of fluids , 1997 .

[29]  Markus Bussmann,et al.  A piecewise linear approach to volume tracking a triple point , 2007 .

[30]  J S Meredith,et al.  Material Interface Reconstruction in VisIt , 2005 .

[31]  Raphaël Loubère,et al.  A second-order accurate material-order-independent interface reconstruction technique for multi-material flow simulations , 2009, J. Comput. Phys..

[32]  H. Marschall,et al.  voFoam - A geometrical Volume of Fluid algorithm on arbitrary unstructured meshes with local dynamic adaptive mesh refinement using OpenFOAM , 2013, 1305.3417.

[33]  Yong Zhao,et al.  A novel coupled level set and volume of fluid method for sharp interface capturing on 3D tetrahedral grids , 2010, J. Comput. Phys..

[34]  James A. Sethian,et al.  Analysis and applications of the Voronoi Implicit Interface Method , 2012, J. Comput. Phys..

[35]  D. Fletcher,et al.  A New Volume of Fluid Advection Algorithm , 2000 .

[36]  Hyung Taek Ahn,et al.  Adaptive moment-of-fluid method , 2009, J. Comput. Phys..

[37]  William H. Press,et al.  Numerical recipes in C , 2002 .

[38]  E. Kührt,et al.  A volume-of-fluid method for simulation of compressible axisymmetric multi-material flow , 2007, Comput. Phys. Commun..

[39]  Mikhail J. Shashkov,et al.  Reconstruction of multi-material interfaces from moment data , 2008, J. Comput. Phys..

[40]  Jérôme Breil,et al.  A multi-material ReALE method with MOF interface reconstruction , 2013 .

[41]  Yi Sui,et al.  An efficient computational model for macroscale simulations of moving contact lines , 2013, J. Comput. Phys..

[42]  M. Bussmann.  A three-dimensional model of an impacting droplet , 2000 .

[43]  Bernd Hamann,et al.  Material Interface Reconstruction , 2003, IEEE Trans. Vis. Comput. Graph..

[44]  I. Hutchings,et al.  Numerical studies of the influence of the dynamic contact angle on a droplet impacting on a dry surface , 2009 .

[45]  M. Fujita,et al.  Computation of Capillary Interactions among Many Particles at Free Surface , 2013 .