**Science accomplishments to date that have come out of APDEC**

**Pellet Injection**

An experimentally proven method of refueling tokamaks is by pellet
injection. Pellet injection is currently seen as the most likely
refueling technique for ITER. Briefly stated, the main scientific goal
is to achieve a predictive capability for the pellet injection
phenomenon in tokamaks especially ITER. An associated scientific goal is
validation studies of the simulation code against pellet injection
experiments in tokamaks. It was experimentally determined (in
experiments on ASDEX Upgrade tokamak, as well as DIII-D and JET) that
the pellet mass drifts in the outward radial direction, and so pellets
injected on the high field side (HFS) showed a much better penetration
and fueling efficiency than pellets injected on the low field side
(LFS). MHD simulations based on the Chombo AMR package have
qualitatively reproduced the differences between HFS and LFS pellet
injection in a manner consistent with experimental observations \[1\].
Recently, Samtaney et al. \[2\] have developed a magnetic flux
coordinate representation for shaped plasmas. The electron heating was
modeled by instantaneously equilibrating the temperature along flux
surfaces. Preliminary results are consistent with the simulations
discussed above, as well as experimental observations of higher
efficiency of HFS fueling over that of LFS fueling. Currently, we are
extending this work to include a kinetic-based model for nonlocal
electron heat transport.

\[1\] R. Samtaney, S. C. Jardin, P. Colella and D. F. Martin, \"3D
Adaptive mesh refinement simulations of pellet injection in tokamaks\",
Computer Physics Comm., 164:220\--228, 2004.

\[2\] R. Samtaney, P. Colella, T. J. Ligocki and S. C. Jardin,
\"Adaptive Mesh Simulations of Pellet Injection in Tokamaks\", SIAM
Conference on Computational Science and Engineering, Orlando, FL,
February 2005.

**Richtmyer-Meshkov Instability**

The Richtmyer-Meshkov instability (RMI) has been the subject of intense
study due to its importance in inertial confinement fusion. Samtaney
showed that the RMI is suppressed in the presence of a magnetic field
via large scale adaptive mesh ideal MHD simulations \[3\]. It was shown
that the instability is suppressed due to a bifurcation of the vortex
sheet into a contact discontinuity with no vorticity (hence stable), and
bounded by slow or intermediate mode shocks. This work was extended by
Wheatley et al. \[4\] who investigated the early shock refraction phase
in RMI, and obtained several solution branches. The analytical solutions
were in excellent agreement with large scale simulations of the MHD
shock refraction process and were also reported in \[4\]. Furthermore,
it was shown that the vanishing limit of the magnetic field the MHD to
hydrodynamics limit is a singular one. Recently, an analytical solution
to the incompressible single-mode perturbation problem, in the presence
of a magnetic field, was obtained which favorably compared with
linearized compressible MHD simulations \[5\].

\[3\] R. Samtaney, \"Suppression of the Richtmyer-Meshkov instability in
the presence of a magnetic field\", Phys. Fluids, 15(8):L53\--56, 2003.

\[4\] V. Wheatley, D.I. Pullin, and R. Samtaney, \"Regular shock
refraction at an oblique planar density interface in
magnetohydrodynamics\", J. Fluid Mech., 522:179\--214, 2005.

\[5\] V. Wheatley, D.I. Pullin, and R. Samtaney, \"Stability of an
impulsively accelerated density interface in magnetohydrodynamics\",
Phy. Rev. Lett. Accepted for publication, 2005. Here are the combustion
and astrophysics science accomplishments from John Bell\'s group from
APDEC. They are in four areas.

**Turbulent premixed flames:**

Many combustion devices are based on turbulent premixed flames because
turbulence produces a convoluted, compact flame with a high density of
energy release. The morphology of the flame surface causes variations in
the chemical reactions that remain a subject of research, as does
turbulence itself. The following papers employ adaptive mesh refinement
to simulate entire laboratory-scale turbulent flames without engineering
models, thus enabling direct comparison with and augmentation of
laboratory experiments. The goal of such research is to characterize the
chemical variability and the mechanisms responsible for it.

J. B. Bell, M. S. Day, I. G. Shepherd, M. Johnson, R. K. Cheng, J. F.
Grcar, V. E. Beckner, M. J. Lijewski, \"Numerical Simulation of a
Laboratory-Scale Turbulent V-flame\", LBNL Report LBNL-54198-Journal,
Proc. Natl. Acad. Sci. USA, 102(29) 10006-10011, 2005. M. S. Day, J. B.
Bell, J. F. Grcar, V. E. Beckner, \"Numerical Control of 3D Turbulent
Premixed Flame Simulations\", LBNL Report LBNL-56882 Ext. Abs., to
appear 20th International Colloquium on the Dynamics of Explosions and
Reactive Systems, July 31-August 5, 2005.

J. B. Bell, M. S. Day, J. F. Grcar, M. J. Lijewski, M. Johnson, R. K.
Cheng, and I. G. Shepherd, \"Numerical Simulation of a Premixed
Turbulent V-Flame\", 19th International Colloquium on the Dynamics of
Explosions and Reactive Systems, July 27-August 1, 2003. J. B. Bell, M.
S. Day, A. S. Almgren, R. K. Cheng, and I. G. Shepherd, \"Numerical
Simulation of Premixed Turbulent Methane Combustion\", Proceedings of
the Second MIT Conference on Computational Fluid and Solid Mechanics,
June 17-20, 2003.

J. B. Bell, M. S. Day, J. F. Grcar, and M. J. Lijewski, \"Analysis of
carbon chemistry in numerical simulations of vortex flame
interactions\", 19th International Colloquium on the Dynamics of
Explosions and Reactive Systems, July 27-August 1, 2003. J. B. Bell, M.
S. Day, and J. F. Grcar, \"Numerical Simulation of Premixed Turbulent
Methane Combustion\", LBNL Report LBNL-49331, Proceedings of the
Combustion Institute, 29:1987-1993 (2002).

**Astrophysics \-- Type Ia Supernovae:**

The nuclear fires in Type Ia supernovae resemble many terrestrial,
chemical flames in that the sound speed is much larger than the fluid
velocity. As a result the same algorithms can be used to simulate
turbulent premixed flames and Type Ia supernovae. The following papers
explore the basic physics of the supernovae with a focus on the
transition to distributed burning in Rayleigh-Taylor unstable flames.
The behavior of the flame near this transition, which cannot be
represented with standard nuclear flame models used in astrophysics, is
important to understanding whether the star can transition to a
detonation. The most recent paper also characterizes the spectral
structure of the turbulence generated by these types of flames. The
turbulent scaling behavior is one the governing factors that controls
the speed of the deflagration, which in turn controls the mechanics of
how the star explodes.

M. Zingale, S. E. Woosley, C.A. Rendleman, M. S. Day, and J. B. Bell,
\"Three-dimensional Numerical Simulations of Rayleigh-Taylor Unstable
Flames in Type Ia Supernovae\", LBNL Report LBNL-56966, accepted,
Astrophysical Journal, 2005.

J. B. Bell, M. S. Day, C. A. Rendleman, S. E. Woosley, and M. A.
Zingale, \"Direct Numerical Simulations of Type Ia Supernovae Flames II:
The Rayleigh-Taylor Instability\", LBNL Report LBNL-54300, Astrophysical
Journal, 608, 883-906, 2004.

J. B. Bell, M. S. Day, C. A. Rendleman, S. E. Woosley, and M. A.
Zingale, \"Direct Numerical Simulations of Type Ia Supernovae Flames I:
The Landau-Darrieus Instability\", LBNL Report LBNL-54088, Astrophysical
Journal, 606, 1029-1038, 2004.

J. B. Bell, M. S. Day, C. A. Rendleman, S. E. Woosley, and M. A.
Zingale, \"Adaptive low Mach number simulations of nuclear flame
microphysics\", LBNL Report 52395, J. Comp. Phys, 195, 677-694, 2004.

**Nitrogen emissions from biomass combustion:**

Biomass fuels are an important way to reduce greenhouse gases because
they close the carbon cycle. Some countries including that of our
experimental collaborators in Denmark already burn substantial
quantities of biomass. However, since plant matter contains significant
amounts of nitrogen, biomass combustion may entail greater NOx pollution
than cleaner fuels. This series of papers capitalizes on the
efficiencies of adaptive mesh refinement to simulate flames with the
very large numbers of reactions needed to study the oxidation chemistry
of fuel-bound nitrogen. Specific topics are examined and validated by
comparing simulations and experiments, namely: the role of species
transport on NOx production in diffusion flames, the accuracy of methods
for reducing raw laser diagnostics into images (PLIF), and bistable
modes of NOx production governed by fluid mixing at moderate
temperatures.

J. F. Grcar, P. Glarborg, J. B. Bell, M. S. Day, A. Loren, and A. D.
Jenson, \"Effects of Mixing on Ammonia Oxidation in Combustion
Environments at Intermediate Temperatures\", LBNL Report LBNL-54187,
Proceedings of the Combustion Institute, 30, 1193-1200, 2004.

J. B. Bell, M. S. Day, J. F. Grcar, W. G. Bessler, C. Shultz, P.
Glarborg, and A. D. Jensen, \"Detailed Modeling and Laser-Induced
Fluorescence Imaging of Nitric Oxide in an NH3-seeded non-premixed
methane/air flame\", LBNL Report LBNL-49333, Proceedings of the
Combustion Institute, 29:2195-2202 (2002).

N. Sullivan, A. D. Jensen, P. Glarborg, M. S. Day, J. F. Grcar, J. B.
Bell, C. J. Pope, and R. J. Kee, \"Ammonia Conversion and NOx Formation
in Laminar Coflowing Nonpremixed Methane-Air Flames\", LBNL Report
LBNL-49347, Combustion and Flame 131(3):285-298 (2002).

**Combustion Diagnostics:**

As first-principles simulations of laboratory-scale flames become
available, it is necessary to have tools of analysis besides
visualization that can draw detailed conclusions from the simulation
data. This series of papers describes two analytical methods for flames
in-silico. Stochastic particle algorithms implement a mathematical probe
to trace atoms through a flame. Reaction path tools automate the
analysis of chemical pathways in simulation data.

J. F. Grcar, M. S. Day, J. B. Bell, \"A Taxonomy of Integral Reaction
Path Analysis\", LBNL Report LBNL-56772, submitted, Combust. Theory
Modelling, 2004.

J. B. Bell, M. S. Day, and J. F. Grcar, M. J. Lijewski, \"Stochastic
Algorithms for the Analysis of Numerical Flame Simulations\", LBNL
Report LBNL-49326-Journal, J. Comp. Phys., 202, 262-280, 2004.

J. F. Grcar, M. S. Day, and J. B. Bell, \"Conditional and opposed
reaction path diagrams for the analysis of fluid-chemistry
interactions\", LBNL Report LBNL-52164, 19th International Colloquium on
the Dynamics of Explosions and Reactive Systems, July 27-August 1, 2003.