Overview and exemplify multiphase code GMFIX

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Hunting for the Deterministic Template(s) Three
General Themes

• Overview and exemplify multiphase code GMFIX
• Hyberbolic-only approach
• Possible directions

(In the Hollow of a Wave at Kanagawa, Hokusai)
"No one believes the results of computational
fluid dynamics except the one who performed the
calculations, and everyone believes experimental
results except the one who performed the
experiment."
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GMFIX(Geophysical Multiphase Flow with
Interphase eXchanges)

• George W. Bergantz, Josef Dufek
• University of Washington
• Sebastian Dartevelle, W.I. Rose
• Michigan Institute of Technology

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KFIX to MFIX to GMFIX

• Eulerian-Eulerian non-equilibrium multiphase,
  3-d, non-steady, enthalpy, reactions
• 2) SIMPLE algorithm, 2d order accurate
  discretization, under-relaxation, variable
  time-step, iterative linear eq solvers SOR and
  conjugate gradient
• 3) F90, SMP or DMP (MPICH) parallel

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KFIX to MFIX to GMFIX (contd.)

• 4) Convergence criteria- accept only part of
  solution that does not change with a factor 10
  increase in tolerance
• 5) (V)LES, static Smagorinsky
• 6) Well validated for fluidized beds at bench
  scales- but at geological scales to be discussed

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Our Focus- Improvements in Physics Essential to
Validation

1. Reaction-entrainment
2. Numerical improvements, e.g. adaptive gridding
3. Multiphase-turbulence-sedimentation models

(Fuji View, Hiroshige)
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Granular Flow Regimes

• Elastic Regime Plastic Regime Viscous Regime
• Stagnant Slow flow Rapid flow
• Stress is strain Strain rate Strain rate
  dependent independent dependent
• Elasticity Soil mechanics Kinetic theory

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Remarks on multiphase flow features

1. Empirical, complex inter-andwithin phase
   momentum transfer equations allow particle volume
   fraction to vary significantly
2. But significant challenges for VLES in
   sedimentation and boundary region

(Dragon Escaping on Smoke from Mt. Fuji, Hokusai)
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Remarks on multiphase flow features (contd.)
In general, fallout of suspended pyroclasts
seems reasonably well understood. (1997)

• "Stokes number is the key dimensionless number
  for the dynamics of relative particle motions in
  the global flow parameterization." Kaminski
  Jaupart (1997)

• Stokes number can dramatically influence
  sedimentation (Burgisser Bergantz, 2002) gives
  rise to meso-scale structures
• 2) Turbulence intensity enhanced or attenuated by
  particles
• Both challenging to address in a numerical model

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Boundary ConditionsNo-slip at the
groundFree-slip at all the other boundariesMass
inflow at the ventVy 200m/sT 900Kes
0.1100 of magmatic water at the vent
Plinian Column Model
Initial Conditions Vent radius 400m Particle
50mm, 1500kg/m3 Dry atmosphere, 298K, 105
Pa Tropopause between 11km and 19km Stratospheric
T_gradient -7K/km

• Geometrical setup
• Cylindrical
• Y 50km height, 100m
• X 65km radial, 100m to 1000m
• Z 51km arc length, q 1rad

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3 min
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30 min
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1 hour
25 m/s
5 m/s
60 m/s
120 m/s
2 m/s
0 m/s
1.5 m/s
-3 m/s
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1 hour
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Plinian column modeling Our results are in a
good agreement - with satellite observations of
the undercooling at the top of the Plinian cloud
(both in magnitude and with time) - with
experimental data and previous numerical modeling
of buoyant plume (velocity profiles, density
profiles, )
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• Plinian column modeling
• However, the details of the cloud dynamic reveal
  unsuspected phenomena
• Complex velocity and density distribution within
  the column
• Positive buoyancy on the edges of the column
  (where it is the most turbulent), while the core
  is collapsing
• Presence of giant vertical vortices
• Non-homogenous temperature profiles within the
  plume (undercooled pockets)
• The overall altitude is time-dependent and
  fluctuates with time
• Complex pressure distribution profiles with time

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Hyperbolic MethodsRandy LeVeque, CLAWPACK

1. Advective terms only, excellent for shocks or
   front tracking.
2. Fast, explicit (but semi-implicit coming)
3. Perhaps a terrific tool for field, rapid laptop
   assessment

(Red Fuji, Hokusai)
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Collapsing plume, parabolic initial shape200 x
200 grid
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Future Directions

1. Invite and enable community with regular
   workshops, dialog, mutual support
2. Hierarchical modeling tools

(Mount Asama, Hiroshige, 1859)

• Towards a universal multi-phase, multi-species
  flow codes applied to geophysical-volcanological
  problems
• It can be used for highly-loaded situations
  (turbidities, pyroclastic flows) and for dilute
  ones (pyroclastic surges, plinian column,
  co-ignimbrites)
• It does not assume unrealistic physical
  conditions it is based on a well accepted
  physics (Navier-Stokes, continuity, 2nd law of
  Mechanics, 1st law of thermodynamic)

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Future Directions

• Development of a water micro-physics model
  (evaporation-condensation-sublimation)
• Development of a complete sub-grid multi-phase
  turbulence model (in collaboration with DOE labs,
  NETL/ORNL)
• Development of a multi-grain size model (for
  unimodal grain-size distribution)
• Development of better viscous dissipation
  algorithms for shock waves/fronts

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