Overview and exemplify multiphase code GMFIX

Hyberbolic-only approach

Possible directions

"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."

(In the Hollow of a Wave at Kanagawa, Hokusai)

Hunting for the Deterministic Template(s)Three General Themes:

GMFIX(Geophysical Multiphase Flow with

Interphase eXchanges)

George W. Bergantz, Josef DufekUniversity of Washington

Sebastian Dartevelle, W.I. RoseMichigan Institute of Technology

KFIX to MFIX to GMFIX1) Eulerian-Eulerian non-equilibrium

multiphase, 3-d, non-steady, enthalpy, reactions

2) SIMPLE algorithm, 2’d order accurate discretization, under-relaxation, variable time-step, iterative linear eq solvers: SOR and conjugate gradient

3) F90, SMP or DMP (MPICH) parallel

KFIX to MFIX to GMFIX (cont’d.)

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…

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)

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

Remarks on multiphase flow features

1) Empirical, complex inter-and–within 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)

Remarks on multiphase flow features (cont’d.)

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

“In general, fallout of suspended pyroclasts seems reasonably well understood.” (1997)1) 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

Geometrical setup:CylindricalY = 50km height, 100mX = 65km radial, 100m to 1000mZ = 51km arc length, = 1rad

Initial Conditions:

Vent radius = 400m

Particle 50m, 1500kg/m3

Dry atmosphere, 298K, 105 Pa

Tropopause between 11km and 19km

Stratospheric T_gradient = -7K/km

Boundary Conditions:No-slip at the groundFree-slip at all the other boundariesMass inflow at the vent:Vy = 200m/sT = 900Ks = 0.1%100% of magmatic water at the vent

Plinian Column Model

3 min …

30 min …

1 hour …

25 m/s 5 m/s

0 m/s

120 m/s

60 m/s

2 m/s

1.5 m/s

-3 m/s

1 hour …

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, …)

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

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)

Collapsing plume, parabolic initial shape200 x 200 grid

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)

• 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

Future Directions