# free-surface-1

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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
– New interface is found by       – New interface is
fitting curve through             approximated by using
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

F
 U   F  0
t
Volume Tracking -

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

– 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

– 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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