A hybrid particle level set method for improved interface capturing

In this paper, we propose a new numerical method for improving the mass conservation properties of the level set method when the interface is passively advected in a flow field. Our method uses Lagrangian marker particles to rebuild the level set in regions which are underresolved. This is often the case for flows undergoing stretching and tearing. The overall method maintains a smooth geometrical description of the interface and the implementation simplicity characteristic of the level set method. Our method compares favorably with volume of fluid methods in the conservation of mass and purely Lagrangian schemes for interface resolution. The method is presented in three spatial dimensions.

[1]  F. Harlow,et al.  Numerical Calculation of Time‐Dependent Viscous Incompressible Flow of Fluid with Free Surface , 1965 .

[2]  F. Harlow,et al.  THE MAC METHOD-A COMPUTING TECHNIQUE FOR SOLVING VISCOUS, INCOMPRESSIBLE, TRANSIENT FLUID-FLOW PROBLEMS INVOLVING FREE SURFACES , 1965 .

[3]  Numerical calculation of surface waves: a modified ZUNI code with surface particles and partial cells , 1973 .

[4]  S. Zalesak Fully multidimensional flux-corrected transport algorithms for fluids , 1979 .

[5]  C. W. Hirt,et al.  Volume of fluid (VOF) method for the dynamics of free boundaries , 1981 .

[6]  P. Smolarkiewicz The Multi-Dimensional Crowley Advection Scheme , 1982 .

[7]  J. Sethian Curvature and the evolution of fronts , 1985 .

[8]  J. Sethian,et al.  Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations , 1988 .

[9]  James A. Sethian,et al.  Numerical Methods for Propagating Fronts , 1987 .

[10]  P. Concus,et al.  Variational Methods for Free Surface Interfaces , 1987 .

[11]  S. Osher,et al.  Algorithms Based on Hamilton-Jacobi Formulations , 1988 .

[12]  P. Colella,et al.  A second-order projection method for the incompressible navier-stokes equations , 1989 .

[13]  S. Osher,et al.  Efficient implementation of essentially non-oscillatory shock-capturing schemes,II , 1989 .

[14]  G. Tryggvason,et al.  A front-tracking method for viscous, incompressible, multi-fluid flows , 1992 .

[15]  Giovanni Lapenta,et al.  Dynamic and selective control of the number of particles in kinetic plasma simulations , 1994 .

[16]  S. Zaleski,et al.  Modelling Merging and Fragmentation in Multiphase Flows with SURFER , 1994 .

[17]  S. Osher,et al.  A level set approach for computing solutions to incompressible two-phase flow , 1994 .

[18]  Peter E. Raad,et al.  The Introduction of Micro Cells to Treat Pressure in Free Surface Fluid Flow Problems , 1995 .

[19]  J. Sethian,et al.  A Fast Level Set Method for Propagating Interfaces , 1995 .

[20]  Peter E. Raad,et al.  Velocity Boundary Conditions for the Simulation of Free Surface Fluid Flow , 1995 .

[21]  W. Rider,et al.  Stretching and tearing interface tracking methods , 1995 .

[22]  John Joseph Helmsen,et al.  A comparison of three dimensional photolithography simulators , 1995 .

[23]  Andrew S. Glassner,et al.  Principles of Digital Image Synthesis , 1995 .

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

[25]  J A Sethian,et al.  A fast marching level set method for monotonically advancing fronts. , 1996, Proceedings of the National Academy of Sciences of the United States of America.

[26]  Peter E. Raad,et al.  The surface marker and micro cell method , 1997 .

[27]  Ann S. Almgren,et al.  An adaptive level set approach for incompressible two-phase flows , 1997 .

[28]  E. Puckett,et al.  A High-Order Projection Method for Tracking Fluid Interfaces in Variable Density Incompressible Flows , 1997 .

[29]  D. B. Kothe,et al.  Convergence and accuracy of kernel-based continuum surface tension models , 1998 .

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

[31]  S. Osher,et al.  A PDE-Based Fast Local Level Set Method 1 , 1998 .

[32]  S. Osher,et al.  An improved level set method for incompressible two-phase flows , 1998 .

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

[34]  D. B. Kothe,et al.  Approximating interfacial topologies with applications for interface tracking algorithms , 1999 .

[35]  J. A. Sethian,et al.  Fast Marching Methods , 1999, SIAM Rev..

[36]  S. Osher,et al.  Regular Article: A PDE-Based Fast Local Level Set Method , 1999 .

[37]  James A. Sethian,et al.  Level Set Methods and Fast Marching Methods , 1999 .

[38]  Mark Sussman,et al.  An Efficient, Interface-Preserving Level Set Redistancing Algorithm and Its Application to Interfacial Incompressible Fluid Flow , 1999, SIAM J. Sci. Comput..

[39]  R. Fedkiw,et al.  A numerical method for two-phase flow consisting of separate compressible and incompressible regions , 2000 .

[40]  M. Sussman,et al.  A Coupled Level Set and Volume-of-Fluid Method for Computing 3D and Axisymmetric Incompressible Two-Phase Flows , 2000 .

[41]  David J. Torres,et al.  The point-set method: front-tracking without connectivity , 2000 .

[42]  Danping Peng,et al.  Weighted ENO Schemes for Hamilton-Jacobi Equations , 1999, SIAM J. Sci. Comput..

[43]  Ronald Fedkiw,et al.  A Boundary Condition Capturing Method for Multiphase Incompressible Flow , 2000, J. Sci. Comput..

[44]  J. Sethian Evolution, implementation, and application of level set and fast marching methods for advancing fronts , 2001 .

[45]  S. Osher,et al.  Level set methods: an overview and some recent results , 2001 .

[46]  Y. L. Zhang,et al.  3D Impact and Toroidal Bubbles , 2001 .

[47]  Ronald Fedkiw,et al.  Practical animation of liquids , 2001, SIGGRAPH.

[48]  Stojan Petelin,et al.  Coupling of the interface tracking and the two-fluid models for the simulation of incompressible two-phase flow , 2001 .

[49]  D. Juric,et al.  A front-tracking method for the computations of multiphase flow , 2001 .

[50]  Ronald Fedkiw,et al.  Animation and rendering of complex water surfaces , 2002, ACM Trans. Graph..

[51]  Ronald Fedkiw,et al.  Level set methods and dynamic implicit surfaces , 2002, Applied mathematical sciences.