Discussion Slides

S.E. Kruger, J.D. Callen, J. Carlson, C.C. Hegna, E.D. Held, T. Jenkins, J. Ramos,

D.D. Schnack, C.R. Sovinec, D.A. Spong

ORNL SWIM MeetOctober 15, 2007

Discussion Issues

• Formulation issues• Computational issues

• Applied math issues (esp. numerical accuracy)• Computer science problems (esp. MxN problem)

• Longer term issues

Formulation questions

• Fundamental equation is:

• What is the best way of formulating the problem?• Lots of discussion€

df

dt= C( f ) + Q( f ),

Issues of time dependence impact computer science coupling to be discussed next

• What is the temporal dependence of the source?

• For the plasma parameters thatwe are studying:• Slowing down time is

~100msec-1 sec?• Mod-B changes slow and small

• MHD time scales:

• NIMROD time step ~ 1 A ~1E-7 sec• Tearing mode growth rate ~ 1-100 msec• Total simulation time ~ 100 msec

€

rE +

r v ×

r B = η

r J +

r F e

rf (x, t)

time (s)

En(J)

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07

10-6

10-4

10-2

100

102

104

106

n=2

n=1

n=0 + ss

Possibilities for coupling include minimal coupling to full coupling

• Assume Frf is ~constant in shape over simulation time• Coupling procedure:

• Calculate Frf(x) from same equilibrium file that NIMROD uses

• NIMROD reads Frf(x) and uses it like phenomenological sources (include such time dependence as phasing)

• Assume Frf is much slower than NIMROD time step• Need to calculate source as NIMROD runs, but do not

need to do it every time step

• More difficult case: Calculate Frf at every time step

• Propose: Start with first step, dump n=0 fields as simulation advances, perform ray tracing on it, see how Frf(x,t) changes in time

FluidProcessors

Processor Elements

Computer Science Issues for Full Scale Coupling Require a Solution to the MxN problem

• Need to give fields (B,n,T) on multiple processors to ray tracing code in format that it understands

• Possible solutions:• File based: Unlikely to work for anything but

the loosest coupling• MPI-based that is hand-coded:

• Very doable (see next slide)• MCT or other parallel coupling toolkit package

• Overkill for this problem, but for long term gains?

Ray Tracing

(Assumed serial)

FluidProcessors Closure

ProcessorsFluid

ProcessorsClosure

Processors

Processor Elements

Processor Elements

NIMROD already has solution for MxN problem for CEL closures

€

q|| =neqv th

π 3 / 2K(L',L) T(−L') − T(L')[ ]∫ dL'

• Recall for of CEL closure:

• Each integration is independent -- trivially parallizable• Difficulties are in load balancing as related to temporal advance• Exact same coding can be used to do ECCD ray tracing

Implementation Details

• What codes are we coupling?• NIMROD• GENRAY?

• Does it handle island geometry?• Should we write one from scratch using the CEL

machinery?

Numerical issues for closure

• Synchronization/numerical stability issues• Closure relation used in MHD code at time t, but based on field data from t - t (or earlier)• Is it adequate to only update closure relation at every N (>1) timesteps rather than every time step?

• Computational readiness issues• Data connections/interfaces need to be developed between MHD code and closure relation code and vice

versa• Feasibility of calculating closure relations in real-time with time-evolving MHD code vs. computing closure

relation offline for a few “typical” NTM cases and fitting to a model

• Island detection and separatrix tracking• Could save time by allowing closure relation calculations to focus only on regions interior to islands rather

than entire plasma volume

• Issues specific to collisional particle models• Need to run finite time interval to get beyond startup transient => collisional quasi-equilibrium• Need to test warm restarts from previous time step• Noise reduction/filtering/smoothing methods (GLRA SVD, spline fit) required in going from discrete particle

data back to MHD equations

• Form of closure relation• Provide viscosity (stress) tensor - maintains consistency with flow velocities from MHD model• “Black box” closure relation - only supplies pressure tensor - possibly consistent with MHD flows after

many time steps, but not at a detailed level

Longer term issues

• ITER has more than ECCD • Lower hybrid CD and Ion Cyclotron CD• Lower Hybrid

• LHCD produces a long tail on electrons. What to do for closure consistency?

• ICRF• Moment approach definitely not OK• Hot particle closure would work (?)• Lots of overlap with the energetic particle SciDAC here

• Can they handle island geometry?

• Our goal should be for full ITER simulation capability, but lots of details are buried here• Need improved Fokker-Planck codes• Sensitivity to hot particle distribution functions

(ref. Diego’s work)• MxN issues between full-wave codes and MHD codes• Island effects in full wave codes?

Near term issues

• Let’s get Frf(x) from a ray tracing code ASAP• What code we use?• Where do we get Qnl?