A grid based particle method for moving interface problems

We propose a novel algorithm for modeling interface motions. The interface is represented and is tracked using quasi-uniform meshless particles. These particles are sampled according to an underlying grid such that each particle is associated to a grid point which is in the neighborhood of the interface. The underlying grid provides an Eulerian reference and local sampling rate for particles on the interface. It also renders neighborhood information among the meshless particles for local reconstruction of the interface. The resulting algorithm, which is based on Lagrangian tracking using meshless particles with Eulerian reference grid, can naturally handle/control topological changes. Moreover, adaptive sampling of the interface can be achieved easily through local grid refinement with simple quad/oct-tree data structure. Extensive numerical examples are presented to demonstrate the capability of our new algorithm.

[1]  Vlastislav Červený,et al.  Ray method in seismology , 1977 .

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

[3]  Said I. Abdel-Khalik,et al.  Accurate representation of surface tension using the level contour reconstruction method , 2005 .

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

[5]  J. E. Hilliard,et al.  Free Energy of a Nonuniform System. I. Interfacial Free Energy , 1958 .

[6]  Thomas Y. Hou,et al.  Boundary integral methods for multicomponent fluids and multiphase materials , 2001 .

[7]  Stanley Osher,et al.  A Hybrid Method for Moving Interface Problems with Application to the Hele-Shaw Flow , 1997 .

[8]  Stanley Osher,et al.  A Fixed Grid Method for Capturing the Motion of Self-Intersecting Wavefronts and Related PDEs , 2000 .

[9]  Frédéric Gibou,et al.  A second order accurate level set method on non-graded adaptive cartesian grids , 2007, J. Comput. Phys..

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

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

[12]  Shingyu Leung,et al.  A level set based Eulerian method for paraxial multivalued traveltimes , 2004 .

[13]  J. Strain.  Tree Methods for Moving Interfaces , 1999 .

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

[15]  J. Cahn,et al.  A microscopic theory for antiphase boundary motion and its application to antiphase domain coasening , 1979 .

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

[17]  Ted Belytschko,et al.  A vector level set method and new discontinuity approximations for crack growth by EFG , 2002 .

[18]  J. Steinhoff,et al.  A New Eulerian Method for the Computation of Propagating Short Acoustic and Electromagnetic Pulses , 2000 .

[19]  P. Lancaster,et al.  Surfaces generated by moving least squares methods , 1981 .

[20]  Jean-David Benamou,et al.  An Introduction to Eulerian Geometrical Optics (1992–2002) , 2003, J. Sci. Comput..

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

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

[23]  Xiaolin Li,et al.  Simple front tracking , 1999 .

[24]  E. P. Ferreira,et al.  The interactions of π - -mesons with complex nuclei in the energy range (100–800) MeV. III. The interaction lengths and elastic scattering of 300 MeV π - -mesons in G5 emulsion , 1959 .

[25]  Xiaolin Li,et al.  Robust Computational Algorithms for Dynamic Interface Tracking in Three Dimensions , 1999, SIAM J. Sci. Comput..

[26]  David E. Womble,et al.  A front-tracking method for multiphase free boundary problems , 1989 .

[27]  P. Koumoutsakos,et al.  A Lagrangian particle level set method. , 2005 .

[28]  Stanley Osher,et al.  Geometric Optics in a Phase-Space-Based Level Set and Eulerian Framework , 2002 .

[29]  C. Pozrikidis,et al.  Interfacial dynamics for Stokes flow , 2001 .

[30]  Jon Louis Bentley,et al.  Quad trees a data structure for retrieval on composite keys , 1974, Acta Informatica.