A density-scaled continuum surface force model within a balanced force formulation

We propose a numerical framework which can simulate free surface flows with complex moving interfaces like droplet splashing as minimizing spurious currents. The numerical framework is based on the CLSVOF (coupled level set and volume-of-fluid) method, the THINC/WLIC (tangent of hyperbola for interface capturing/weighted line interface calculation) scheme, multi-moment methods (CIP-CSL and VSIAM3) and density-scaled CSF (continuum surface force) model within a balanced force formulation. In this paper, we propose a level set based algorithm of the density-scaled balanced CSF model and show that the density-scaled balanced CSF model can reduce spurious currents more than the standard balanced CSF model without using the density-scaling when the exact curvature is not given. We also show that the numerical framework can well capture the physics of droplet splashing.

[1]  Takashi Yabe,et al.  Constructing exactly conservative scheme in a non-conservative form , 2000 .

[2]  J. Li,et al.  Numerical simulation of breakup of a viscous drop in simple shear flow through a volume-of-fluid method , 2000 .

[3]  T. Yabe,et al.  The constrained interpolation profile method for multiphase analysis , 2001 .

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

[5]  Feng Xiao,et al.  A simple algebraic interface capturing scheme using hyperbolic tangent function , 2005 .

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

[7]  T. Yabe,et al.  An Exactly Conservative Semi-Lagrangian Scheme (CIP–CSL) in One Dimension , 2001 .

[8]  T. Yabe,et al.  Conservative and oscillation-less atmospheric transport schemes based on rational functions , 2002 .

[9]  Kensuke Yokoi,et al.  Efficient implementation of THINC scheme: A simple and practical smoothed VOF algorithm , 2007, J. Comput. Phys..

[10]  Kensuke Yokoi,et al.  A practical numerical framework for free surface flows based on CLSVOF method, multi-moment methods and density-scaled CSF model: Numerical simulations of droplet splashing , 2013, J. Comput. Phys..

[11]  Feng Xiao,et al.  Unified formulation for compressible and incompressible flows by using multi-integrated moments II: Multi-dimensional version for compressible and incompressible flows , 2006, J. Comput. Phys..

[12]  J. Brackbill,et al.  A continuum method for modeling surface tension , 1992 .

[13]  Kensuke Yokoi.  Numerical method for a moving solid object in flows. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[14]  Feng Xiao,et al.  Revisit to the THINC scheme: A simple algebraic VOF algorithm , 2011, J. Comput. Phys..

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

[16]  Bernhard Weigand.  Reduction of parasitic currents in the DNS VOF code FS3D , 2010 .

[17]  Mark Sussman,et al.  A Stable and Efficient Method for Treating Surface Tension in Incompressible Two-Phase Flow , 2009, SIAM J. Sci. Comput..

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

[19]  Detlef Lohse,et al.  Drop impact upon micro- and nanostructured superhydrophobic surfaces. , 2009, Langmuir : the ACS journal of surfaces and colloids.

[20]  Jie Li,et al.  Calcul d'Interface Affine par Morceaux , 1995 .

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

[22]  J. Brock,et al.  Volume tracking of interfaces having surface tension in two and three dimensions , 1996 .

[23]  H. Udaykumar,et al.  Sharp interface Cartesian grid method II: A technique for simulating droplet interactions with surfaces of arbitrary shape , 2005 .

[24]  Kensuke Yokoi,et al.  A Numerical Method for Free-Surface Flows and Its Application to Droplet Impact on a Thin Liquid Layer , 2008, J. Sci. Comput..

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

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

[27]  Kensuke Yokoi,et al.  Numerical method for complex moving boundary problems in a Cartesian fixed grid. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[29]  Mark Sussman,et al.  A sharp interface method for incompressible two-phase flows , 2007, J. Comput. Phys..

[30]  I. Hutchings,et al.  Numerical studies of the influence of the dynamic contact angle on a droplet impacting on a dry surface , 2009 .

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

[32]  Kensuke Yokoi,et al.  Numerical studies of droplet splashing on a dry surface: triggering a splash with the dynamic contact angle , 2011 .

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

[34]  Feng Xiao,et al.  A Finite-Volume Grid Using Multimoments for Geostrophic Adjustment , 2006 .

[35]  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..

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

[37]  肖锋,et al.  Revisit To the Thinc Scheme: A Simple Algebraic VOF Algorithm , 2011 .

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

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

[40]  F. Xiao,et al.  Numerical simulations of free-interface fluids by a multi-integrated moment method , 2005 .

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

[42]  Feng Xiao,et al.  An interface capturing method with a continuous function: The THINC method with multi-dimensional reconstruction , 2012, J. Comput. Phys..

[43]  J. Mostaghimi,et al.  A semi‐implicit finite volume implementation of the CSF method for treating surface tension in interfacial flows , 2009 .