Transcript BOUT++ Towards an MHD Simulation of ELMs

BOUT++
Towards an MHD Simulation of ELMs
B. Dudson and H.R. Wilson
Department of Physics, University of York
M.Umansky and X.Xu
Lawrence Livermore National Laboratory, CA
P.Snyder
General Atomics, San Diego, CA
Outline
• BOUT++: motivation and philosophy
• ELM modelling: the approach and objectives
• Initial benchmarking results (work in progress), and future aims
BOUT++: Philosophy
• BOUT++ is a collaborative project between University of York
and LLNL
• The code provides a framework for developing plasma fluid
codes:
– user defined magnetic geometry (in terms of metrics)
– user-defined plasma model:
f
 A f
t
• Flexible, user-friendly code (small compromise on speed)
– easy to adjust plasma physics model, and explore implications
Example of the code: Ideal MHD equations
dndt = -n*Div(v) – V_dot_Grad(v,n)
dpdt = –V_dot_Grad(v,p) - gamma*p*Div(v)
dvdt = –V_dot_Grad(v,v) + ((Curl(B)^B) - Grad(p))/n
dBdt = Curl(v^B)
Physics Objectives
• There are two main objectives:
• Edge turbulence modelling
• Edge MHD and ELMs
– focus on the ELM modelling here
ELM modelling- the approach
• Two complementary approaches to tackle the ELM problem
• Full non-ideal MHD code, towards a model for the ELM crash
– A range of codes being used: NIMROD, BOUT, JOREK, M3D, etc
– Advantage: well-developed codes, some with 2-fluid effects
– Disadvantage: difficult to pull out and and study the impact of specific
physics elements without a detailed knowledge of the code; making contact
with analytic theory is not easy
• Building up from simple ideal MHD model
– Basic ideal MHD model eases comparison with analytic theory and linear
codes (eg ELITE and non-linear ballooning theory)
– The model can then be slowly built up, monitoring the impact of different
physics effects
• BOUT++ is ideally suited to exploring the second approach
– permits the user to add and subtract physics in a clear way
Initial benchmark studies (in progress)
• The Orszag-Tang vortex provides a “standard” test of 2D ideal
MHD solvers: looks good, qualitatively
• Tests the ability to treat shocks (possibly important for ELMs)
Athena, Roe solver
BOUT++, ideal MHD
Quantitative Benchmark: linear ideal MHD
• We have begun to test the code against ELITE
• For initial tests, we have implemented a reduced ideal MHD
model into BOUT++
– Valid for high-n ballooning modes
• Initial case: strong instability, with significant peeling component:
– OK for intermediate n, but unable to reproduce higher n (yet)
– Points to a problem with the kink/peeling drive (sensitive to plasmavacuum boundary)
Produces “fingers” in non-linear regime
• Mode propagates radially
•Filamentary structures are produced in the non-linear regime
• Cannot take too seriously while there is disagreement in the
linear regime
– but encouraging first signs!
n=10
New equilibrium to minimise coupling to vacuum
• Presently exploring a more ballooning case, with reduced
coupling to vacuum (ELITE requires some edge interaction)
• ELITE predicts close to marginal stability: g/wA=0.01
Equilibrium mesh
ELITE
The challenges of marginal stability
• Agreement has not yet been achieved (the BOUT++ runs take 12 hours, while
ELITE is ~3 minutes, so comparisons are not trivial)
• It is necessary to work close to linear marginal stability
– it is the experimentally relevant situation (p‘ increases slowly through
marginal stability
– modes that are strongly unstable linearly are likely to have different
dynamics
– existing non-linear theories are based on proximity to marginal stability
• One issue with proximity to marginal stability is resolution of fine-scale
structures near rational surfaces
– makes sense to use nq as the radial variable to improve resolution
around rational surfaces (pack mesh there): presently exploring this
• When we go non-linear, an additional challenge will be the time taken to get
into the non-linear regime
– will need to make use of scaling of mode structure during linear phase to
speed code up here
Future plans: the strategy
• Work to find a mesh and formalism that gives agreement with
ELITE close to marginal stability with weak coupling to vacuum
• Extend/return to linear tests where mode couples to vacuum
• Extend to non-linear regime
– compare non-linear evolution with and without kinkcomponent
• Extend to include non-ideal physics (care: unphysical modes can
be introduced when dissipation is introduced…diamagnetic effects
will be an important first effect to include).