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					Free Surface Modeling
                                            Outline

   Engineering Applications
   Moving Boundary Methods
    – Lagrangian
    – Eulerian
   Flux Line-Segment Model for Advection and
    Interface Reconstruction (FLAIR)
   Hybrid Finite Element-Volume of Fluid
   Simulations
                           Sample Applications

   Crystal Growth

   Molding/Casting

   Liquid Free Surfaces

   Flame Propagation
                        Moving Boundary Methods


   Lagrangian Methods               EulerianMethods
    – Grid is Adaptive                – Grid is fixed
    – Points on interface are         – Fluid under interface is
      advected                          advected
    – New interface is found by       – New interface is
      fitting curve through             approximated by using
      advected points                   volume fraction variable
                               Some Specific Methods

   Lagrangian Type
    – Moving Grid
    – Front Tracking
   Eulerian Type
    – Marker and Cell (MAC)
    – Volume-of-Fluid (VOF)
       »   Surface Line Interface Calculation (SLIC)
       »   Hirt & Nichols VOF
       »   Young’s VOF
       »   FLAIR
       »   Many other versions exist
                                                                       Moving Grid Methods

           Rayleigh-Taylor
            Instability

           Interface coincides
            with cell boundaries

           Distorted Grid over
            time


Example from Approaches to Resolving and Tracking Interfaces and Discontinuities, Laskey et. al, NRL Report 5999, 7/28/97
                       Front Tracking Methods

   Points defined on Interface
    and are moved in time

   Interface location and
    orientation is known at each
    time step

   Method fails when interface    Sample Configuration
    geometry becomes
    complicated
                       MAC (Marker and Cell)

   Massless Particles are
    injected
   Particle Trajectories are
    tracked
   Cannot resolve details of
    the inteface smaller than
    the mesh size
   Expensive in Computer
    time and memory
                   Volume Tracking: General Idea

   Define “fluid volume fraction” : f-field
    – f=0: No fluid in cell
    – f=1: Cell filled with fluid
    – 0<f<1: Cell partially filled with fluid (i.e. Interface cell)

   Initial interface geometry is used to compute
    fractions
                         1       1       1     .68         0

                         1       1       1           .42   0

                         1       1       .92     .09       0

                         1      .85     .35      0         0

                         .31     .09     0       0         0

                          0      0       0       0         0
              Volume Tracking: General Idea

   Interface is reconstructed using the “f-field”
    – f-field does NOT imply a unique interface geometry
    – interface is constructed based on some algorithm


   Volume fractions (f-field) are some-how advected

   New f-field based on amount of fluid entering,
    leaving and reamining in the cell
       Advection of Volume Fraction Field

   Fluid Advection satisfies:
                   F
                       U   F  0
                   t
                             Volume Tracking -
                       Advantages/Disadvantages

   Advantages
    –   Interface positions are NOT stored for each time-step
    –   Large Surface Deformations
    –   Mergering and Breakup of Interfaces
    –   Easy implementation


   Disadvantages
    – Interfaces are NOT exact
    – Reconstruction techniques require many logical operations
    – Resolution dependent
SLIC (Simple Line Interface Calculation)

   Interface is Horz. or Vert.

   Assumed:
    – fluid resides on heavyside        Original Geometry
      of interface


   Advection:
    – x-pass (horizontal)
    – y-pass (vertical)
                                   x-pass           y-pass
                            Hirt & Nichol’s VOF

   Interface is Horz. or Vert.
    (piecewise constant)
    (stair stepped)

   Derivatives of the f-field      Original Geometry

    determine whether the
    interface is Horz. or Vert.

   Derivatives calculated using
    fractional volumes averaged
    over several cells               Reconstructed
                                    Young’s VOF

   Interfaces - piecewise linear

   Interface has slope and is
    fitted within a single cell       Original Geometry


   Interface slope and fluid
    position are determined
    from inspection of 8
    neighboring cells
                                       Reconstructed

				
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posted:3/5/2010
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