A new volume of fluid method in three dimensions—Part II: Piecewise‐planar interface reconstruction with cubic‐Bézier fit

A new interface reconstruction method in 3D is presented. The method involves a conservative level-contour reconstruction coupled to a cubic-Bezier interpolation. The use of the proposed piecewise linear interface calculation (PLIC) reconstruction scheme coupled to a multidimensional time integration provides solutions of second-order spatial and temporal accuracy. The accuracy and efficiency of the proposed reconstruction algorithm are demonstrated through several tests, whose results are compared with those obtained with other recently proposed methods. An overall improvement in accuracy with respect to other recent methods has been achieved, along with a substantial reduction in the central processing unit time required.

[1]  S. Zaleski,et al.  Analytical relations connecting linear interfaces and volume fractions in rectangular grids , 2000 .

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

[3]  M. Rudman,et al.  A 3D unsplit-advection volume tracking algorithm with planarity-preserving interface reconstruction , 2006 .

[4]  S. Zaleski,et al.  Volume-of-Fluid Interface Tracking with Smoothed Surface Stress Methods for Three-Dimensional Flows , 1999 .

[5]  Lingling Wu,et al.  A simple package for front tracking , 2006, J. Comput. Phys..

[6]  Philippe Fraunié,et al.  3D two phase flows numerical simulations by SL‐VOF method , 2004 .

[7]  J. López,et al.  An improved PLIC-VOF method for tracking thin fluid structures in incompressible two-phase flows , 2005 .

[8]  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..

[9]  Alexandre J. Chorin,et al.  Curvature and solidification , 1985 .

[10]  Blair Swartz,et al.  The second-order sharpening of blurred smooth borders , 1989 .

[11]  Seungwon Shin,et al.  Modeling three-dimensional multiphase flow using a level contour reconstruction method for front tracking without connectivity , 2002 .

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

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

[14]  P. Colella,et al.  A conservative three-dimensional Eulerian method for coupled solid-fluid shock capturing , 2002 .

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

[16]  M. Rudman.  INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, VOL. 24, 671–691 (1997) VOLUME-TRACKING METHODS FOR INTERFACIAL FLOW CALCULATIONS , 2022 .

[17]  Eugenio Aulisa,et al.  Interface reconstruction with least-squares fit and split advection in three-dimensional Cartesian geometry , 2007, J. Comput. Phys..

[18]  F. Faura,et al.  A new volume of fluid method in three dimensions—Part I: Multidimensional advection method with face‐matched flux polyhedra , 2008 .

[19]  J. López,et al.  A volume of fluid method based on multidimensional advection and spline interface reconstruction , 2004 .

[20]  D. B. Kothe,et al.  A Parallel, Volume-Tracking Algorithm for Unstructured Meshes , 1996, Parallel CFD.

[21]  S. Zaleski,et al.  DIRECT NUMERICAL SIMULATION OF FREE-SURFACE AND INTERFACIAL FLOW , 1999 .

[22]  Ian M. Mitchell,et al.  A hybrid particle level set method for improved interface capturing , 2002 .

[23]  R. LeVeque.  High-resolution conservative algorithms for advection in incompressible flow , 1996 .