Filament capturing with the Multimaterial Moment-of-Fluid method

A novel method for capturing two-dimensional, thin, under-resolved material configurations, known as "filaments," is presented in the context of interface reconstruction. This technique uses a partitioning procedure to detect disconnected regions of material in the advective preimage of a cell (indicative of a filament) and makes use of the existing functionality of the Multimaterial Moment-of-Fluid interface reconstruction method to accurately capture the under-resolved feature, while exactly conserving volume. An algorithm for Adaptive Mesh Refinement in the presence of filaments is developed so that refinement is introduced only near the tips of filaments and where the Moment-of-Fluid reconstruction error is still large. Comparison to the standard Moment-of-Fluid method is made. It is demonstrated that using filament capturing at a given resolution yields gains in accuracy comparable to introducing an additional level of mesh refinement at significantly lower cost.

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

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

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

[4]  Theo G. Theofanous,et al.  High-fidelity interface tracking in compressible flows: Unlimited anchored adaptive level set , 2007, J. Comput. Phys..

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

[6]  Mark Sussman,et al.  A Discontinuous Spectral Element Method for the Level Set Equation , 2003, J. Sci. Comput..

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

[8]  Benjamin Seibold,et al.  A gradient-augmented level set method with an optimally local, coherent advection scheme , 2009, J. Comput. Phys..

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

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

[11]  Qinghai Zhang,et al.  A new interface tracking method: The polygonal area mapping method , 2008, J. Comput. Phys..

[12]  Mark Sussman,et al.  A Coupled Level Set-Moment of Fluid Method for Incompressible Two-Phase Flows , 2013, J. Sci. Comput..

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

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

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

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

[17]  R. Motte,et al.  Adaptive subdivision piecewise linear interface calculation (ASPLIC) for 2D multi‐material hydrodynamic simulation codes , 2015 .

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

[19]  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..

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

[21]  Rao V. Garimella,et al.  Interface Reconstruction in Multi-fluid, Multi-phase Flow Simulations , 2005, IMR.

[22]  Hongkai Zhao,et al.  A grid based particle method for solving partial differential equations on evolving surfaces and modeling high order geometrical motion , 2011, J. Comput. Phys..

[23]  Hongkai Zhao,et al.  A grid based particle method for moving interface problems , 2009, J. Comput. Phys..

[24]  Suthee Wiri,et al.  On improving mass conservation of level set by reducing spatial discretization errors , 2005 .

[25]  Kenneth I. Joy,et al.  Smooth, Volume-Accurate Material Interface Reconstruction , 2010, IEEE Transactions on Visualization and Computer Graphics.