Adaptive VOF with curvature‐based refinement

Adaptive refinement is implemented in the context of the volume-of-fluid (VOF) methodology in order to study the efficacy of resolving interfaces adaptively based on the local value of curvature. The usual uniform mesh VOF implementation is modified slightly to ensure accurate advection of fluxes between cells at different resolutions. Normals and curvatures are calculated accurately via height functions. Results of a series of tests indicate that in most instances the use of adaptive refinement (when compared to uniform refinement with a similar number of cells) leads to more accurate VOF advection. The results also clearly show that curvature-based adaptive refinement leads to a distribution of errors along an interface that is nearly independent of curvature. Copyright © 2007 John Wiley & Sons, Ltd.

[1]  David P. Schmidt,et al.  Adaptive tetrahedral meshing in free-surface flow , 2005 .

[2]  P. Colella,et al.  An Adaptive Level Set Approach for Incompressible Two-Phase Flows , 1997 .

[3]  Deborah Greaves,et al.  Simulation of viscous water column collapse using adapting hierarchical grids , 2006 .

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

[5]  Michel Visonneau,et al.  Computation of free‐surface flows with local mesh adaptation , 2005 .

[6]  Takahiko Tanahashi,et al.  Numerical analysis of moving interfaces using a level set method coupled with adaptive mesh refinement , 2004 .

[7]  S. Osher,et al.  Spatially adaptive techniques for level set methods and incompressible flow , 2006 .

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

[9]  Deborah Greaves,et al.  A quadtree adaptive method for simulating fluid flows with moving interfaces , 2004 .

[10]  G. Wittum,et al.  Two-Phase Flows on Interface Refined Grids Modeled with VOF, Staggered Finite Volumes, and Spline Interpolants , 2001 .

[11]  Rainald Löhner,et al.  Simulation of flows with violent free surface motion and moving objects using unstructured grids , 2007 .

[12]  Stéphane Zaleski,et al.  Formation de digitations lors de l'impact d'une goutte sur un film liquide , 1998 .

[13]  Philippe A. Tanguy,et al.  A finite element strategy for the solution of interface tracking problems , 2005 .

[14]  Dong-Yol Yang,et al.  Three-dimensional finite element analysis of transient fluid flow with free-surface using marker surface method and adaptive grid refinement , 1999 .

[15]  Hanan Samet,et al.  The Design and Analysis of Spatial Data Structures , 1989 .

[16]  Alistair G.L. Borthwick,et al.  Finite‐volume‐type VOF method on dynamically adaptive quadtree grids , 2004 .

[17]  Andreas Theodorakakos,et al.  Simulation of sharp gas–liquid interface using VOF method and adaptive grid local refinement around the interface , 2004 .

[18]  Deborah Greaves,et al.  Simulation of interface and free surface flows in a viscous fluid using adapting quadtree grids , 2004 .

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

[20]  Markus Bussmann,et al.  Modeling the splash of a droplet impacting a solid surface , 2000 .

[21]  Martin Rieber,et al.  A numerical study on the mechanism of splashing , 1999 .

[22]  Dong-Yol Yang,et al.  Finite element analysis of transient fluid flow with free surface using VOF (volume-of-fluid) method and adaptive grid , 1998 .

[23]  Matthew W. Williams,et al.  A balanced-force algorithm for continuous and sharp interfacial surface tension models within a volume tracking framework , 2006, J. Comput. Phys..

[24]  M. Renardy,et al.  PROST: a parabolic reconstruction of surface tension for the volume-of-fluid method , 2002 .

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