Overview of recent BOUT++ Simulation
and validation results
X. Q. Xu
Lawrence Livermore National Laboratory
Acknowledgement: P.W.Xi1,2, C. H. Ma1,2 , T.Y.Xia1,3, B.Gui1,3, G.Q.Li1,3, J. F. Ma1,4, A.Dimits1, I.Joseph1,
M.V.Umansky1, S.S.Kim5, T.Rhee5, G.Y.Park5, H.Jhang5, P.H.Diamond6,7, B.Dudson8, P.B.Snyder9
1Lawrence
Livermore National Laboratory, Livermore, California 94551, USA
2School of Physics, Peking University, Beijing, China
3Institute of Plasma Physics, Chinese Academy of Sciences, Hefei, China
4Institute for fusion studies, University of Texas, Austin, TX 78712, USA
5WCI Center for Fusion Theory, National Fusion Research Institute, Daejon, South Korea
6CASS and Dept. of Physics, University of California, San Diego, La Jolla, CA, USA
7University of York, Heslington, York YO10 5DD, United Kingdom
8General Atomics, San Diego, California 92186, USA
Presented at
Institute of Plasma Physics, CAS
November 27, 2013, Hefei, China
This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344. LLNL-PRES-645770
Tokamak edge region encompasses boundary layer
between hot core plasma and material walls
 Complex geometry
 Rich physics (plasma, atomic, material)
 Sets key engineering constraints for
fusion reactor
 Sets global energy confinement
Tokamak
interior
BOUT (BOUndary Turbulence) was originally developed at
LLNL in late 1990s for modeling tokamak edge turbulence
BOUT++ is a successor to BOUT,
developed in collaboration with Univ. York*
B UT++
Original BOUT, tokamak applications on boundary
turbulence and ELMs with encouraging results
Boundary Plasma Turbulence Code
BOUT-06: code refactoring using differential operator
approach, high order FD, verification
Gyro-fluid extension
RMPs
Neutrals & impurities
BOUT++: OOP, 2D parallelization, applications to
tokamak ELMs and linear plasmas
2000
•
•
•
•
•
2005
Preconditioner
Computing on GPUs
2013
X.Q. Xu and R.H. Cohen, Contrib. Plasma Phys. 38, 158 (1998)
Xu, Umansky, Dudson & Snyder, CiCP, V. 4, 949-979 (2008).
Umansky, Xu, Dudson, et al., , Comp. Phys. Comm. V. 180 , 887-903 (2008).
Dudson, Umansky, Xu et al., Comp. Phys. Comm. V.180 (2009) 1467.
Xu, Dudson, Snyder et al., PRL 105, 175005 (2010).
BOUT and BOUT++ have been products of broad
international collaborations
Lodestar Research Corporation
Southwestern
Institute of Physics
Institute of plasma Physics
Chinese Academy of Sciences
BOUT++ MAP
Principal Results
 A suite of two-fluid models has been
implemented in BOUT++ for
 all ELM regimes and fluid turbulence
 A suite of gyro-fluid models is under
development for
 pedestal turbulence and transport
 Neutral models
 Fluid neutral models are developed for
• SMBI, GAS puffing, Recycling
 Coupled to EIRENE Monte Carlo code
to follow the neutral particles
 A PIC module for impurity generation and
transport
 A framework for development of
kinetic-fluid hybrid
 A elm size dependence with density or
collisionality for type-I ELMs mainly from
edge bootstrap current and ion diamagnetic
6
stabilization effects
BOUT++: A framework for nonlinear twofluid and gyrofluid simulations
ELMs and turbulence
 Different twofluid and gyrofluid models are developed under BOUT++
framework for ELM and turbulence simulations
Twofluid
Gyrofluid
Physics
3-field
1+0
(𝜛, 𝑃, 𝐴∥ )
(𝑛𝑖𝐺 , 𝑛𝑒 , 𝐴∥ )
Peeling-ballooning
mode
4-field
2+0
(𝜛, 𝑃, 𝐴∥ , 𝑉∥ )
(𝑛𝑖𝐺 , 𝑛𝑒 , 𝐴∥ , 𝑉∥ )
5-field
+ Thermal transport
no acoustic wave
𝜛, 𝑛𝑖 , 𝐴∥ , 𝑇𝑖 , 𝑇𝑒
6-field
𝜛, 𝑛𝑖 , 𝐴∥ , 𝑉∥ , 𝑇𝑖 , 𝑇𝑒
Braginskii equations
+ acoustic wave
3+1
(𝑛𝑖𝐺 , 𝑛𝑒 , 𝐴∥ , 𝑉∥ , 𝑇𝑖⊥ , 𝑇𝑖∥ , 𝑇𝑒 )
Snyder+Hammett’s model
+ additional drift
wave instabilities
+ Thermal transport
7
A good agreement between BOUT++, ELITE and
GATO for both peeling and ballooning modes
cbm18_dens8
A
D
n
• As edge current increases, the
difference between BOUT++ and
GATO/ELITE results becomes large
• This difference is due to the vacuum
treatment
For the real “vacuum” model,
the effect of resistivity should
be included
4-field model agrees well with 3-field
for both ideal and resistive ballooning modes
• ac value from eigenvalue solver agrees with BOUT simulation.
• Non-ideal effects are consistent in both models
 diamagnetic stabilization
 resistive mode with a <ac
 increase n of maximum growth rate with decrease of a
The onset of ELMs 𝜸 > 𝟎 is shifted to 𝜸 > 𝜸𝒄 due to P-B turbulence,
which may explain those unknown questions observed in experiments
 The occurrence of ELMs depends sensitively on the
nonlinear dynamics of P-B turbulence;
 The evolution of relative phase between P-B mode
potential and the pressure perturbations is a key to ELMs
 Phase coherence time 𝝉𝒄 determines the growing time of
an instability by extraction of expansion free energy.
 Nonlinear criterion sets the onset of ELMs
P. W. Xi, X.Q. Xu, P. H. Diamond, submitted to PRL, 2013
 c ~ ln 10 /  c
 c   k  V
2

'

2
D  

1 / 3
 Pˆn  ,  , t  

  n , ,  , t   arg 
 ˆ  ,  , t  
 n

BOUT++ global GLF model agrees well
with gyrokinetic results
• BOUT++ using Beer’s 3+1 model agrees well with gyrokinetic results.
• Non-Fourier method for Landau damping shows good agreement with
Fourier method.
 Implemented in the BOUT++
 Padé approximation for the
modified Bessel functions
 Landau damping
 Toroidal resonance
 Zonal flow closure in progress
 Nonlinear benchmark underway
 Developing the GLF models
 to behave well at large perturbations
 for second-order-accurate closures
 Conducting global nonlinear kinetic
ITG/KBM simulations at pedestal and
collisional drift ballooning mode
across the separatrix in the SOL
Cyclone base case
SS Kim, et al.
Development of flux-driven edge simulation
Edge Transport Barrier formation with external sheared flow
– Heat source inside the separatrix and sink outside the separatrix
– ETB is formed by the externally applied sheared flow, but sometimes triggered by
turbulence driven flow when external flow is zero
SOL diffusion coefficient = 10-6
ExB shearing rate
T=200
T=100
Time
T=0
normalized poloidal flux
normalized poloidal flux
Six-filed simulations show that Ion perturbation has a large initial crash
and electron perturbation only has turbulence spreading
due to inward ExB convection
Te
Ti
6-field module has the capability to simulate the
heat flux in divertor geometry
Left: electron temperature perturbation
[1]X. Q. Xu et al., Commun. Comput. Phys. 4, 949 (2008).
[2]T. Y. Xia et al., Nucl. Fusion 53, 073009 (2013).
Toroidal direction (m)
Toroidal direction (m)
Six-field (ϖ, ni, Ti, Te, A||, V||): based on
Braginskii equations, the density, momentum
and energy of ions and electrons are described
in drift ordering [1,2].
Toroidal direction (m)
Bottom: heat flux structures on toroidal
direction.
R (m)
Inner target
R (m)
R (m)
Outer target Outer mid-plane14
A set of equilibrium with different density profiles
are generated
Collisionality at peak gradient radial position:
Ne (10^19
m^-3)

*
ne
Pressure profile is fixed
1.0
3.0
5.0
7.0
9.0
1.91*10^-3
4.03*10^-2
1.59*10^-1
3.81*10^-1
0.72

*
J bo
As the edge density (collisionality) increases, the growth rate of the
P-B mode increases for high n but decreases for low n (1<n<5)
 S=10^8, SH =10^15, with ion diamagnetic effects and gyro-viscosity.
 As the ballooning term dominates the high n modes, the stabilization effects of the ion diamagnetic drifts become
less important when density is increased.
 The kink term dominates the low n modes. Therefore, as the density increases, the edge current decreases and
growth rate decreases.
 As the edge collisionality increases, the dominant P-B mode shifts to higher n and the width of the dispersion relation
increases.
 The relation between ELM size and collisionality has been shown to have the same trend as the scaling law.
SMBI particle fueling models has been implemented
Physical model – plasmas, atom, molecule
 Nˆ i
 Tˆe
 tˆ
 tˆ
=


c
2
p
p
  || Vˆ||i Nˆ i = Dˆ  i   Nˆ i  Sˆ I  Sˆ rec
Nˆ e  Nˆ i
Quasi-neutral
 2me
2
2 c 2
2

 2
 || ˆ || e  || Tˆe  ˆ  e   Tˆe  ˆ rec Wˆ rec  ˆ I  Tˆe  Wˆ I   ˆ diss Wˆ diss  Wˆ bind  
3
3
3 Nˆ i

 3
 Mi



 Tˆi


2
2
2 c 2
 Vˆ||i  ||Tˆi =
 || ˆ ||i  || Tˆi  Tˆi  ||Vˆ||i  ˆ  i   Tˆi  ˆ rec  ˆ I Tˆi  
 tˆ
3
3
3 Nˆ i

 || Pˆ
 Vˆ|| i
4
1
0
 Vˆ|| i  ||Vˆ|| i =
 || ˆ i  ||Vˆ|| i 
 ˆ CX  ˆ I
 tˆ
3 Nˆ i Mˆ i
Nˆ i Mˆ i



 Nˆ a


B
Vm 0 N m 0
2 m e  Tˆe  Tˆi

M i  ˆe
Vˆ

 Tˆe  Tˆi

 ˆ
e

|| i
 Vˆ|| a
SMBI
ˆ 1  0.65

ˆ 2  1.0
LCFS

c
c
2
p
p
  || Dˆ || a  || Nˆ a  Dˆ  a   Nˆ a   Sˆ I  Sˆ rec  2 Sˆ diss
 tˆ
 Nˆ m
 tˆ
 Vˆ
xm
 tˆ


  x Vˆxm Nˆ m =  Sˆ diss
Nˆ m 0
 x Pˆm
 Vˆxm  xVˆxm = 
Nˆ m Mˆ m
Vˆxm0
Local Const.
Flux Boundary
Simulation qualitatively consistent with Expts.
exp.
sim.
t  0 ms
1 . 0 ms
2 . 0 ms
Ongoing validation of MHD instability data from EAST
BOUT++ simulations show that the stripes from EAST
visible camera match ELM filamentary structures
BOUT++ simulation shows that
the ELM stripe are filamentary
structures*
Z.X.Liu, et al., POSTER SESSION I
0
Z (m)
EAST#41019@3034ms
Visible camera shows bright
ELM structure$
-0.5
2
Major radius
R (m)
2.25
 Pitch angle match!
 Mode number match!
T. Y. Xia, X.Q. Xu, Z. X. Liu, et al, TH/5-2Ra,
24th IEAE FEC, San Diego, CA, USA, 2012
$Photo
*Figure
by J. H. Yang
by W.H. Meyer
Ongoing validation of MHD instability data from KSTAR
The synthetic images from interpretive BOUT++ simulations show the similar patterns as ECEI
H Park, et al., APS DPP invited talk, Nov., 2013
M. Kim, et al., POSTER SESSION I
Principal Results
 A suite of two-fluid models has been
implemented in BOUT++ for
 all ELM regimes and fluid turbulence
 A suite of gyro-fluid models is under
development for
 pedestal turbulence and transport
 Neutral models
 Fluid neutral models are developed for
• SMBI, GAS puffing, Recycling
 Coupled to EIRENE Monte Carlo code
to follow the neutral particles
 A PIC module for impurity generation and
transport
 A framework for development of
kinetic-fluid hybrid
 A elm size dependence with density or
collisionality for type-I ELMs mainly from
edge bootstrap current and ion diamagnetic
21
stabilization effects
BOUT++ background information & websites
The 2013 BOUT++ workshop website,
https://bout2013.llnl.gov
BOUT++ background information and
continuing development on the
following websites:
https://bout.llnl.gov
http://www-users.york.ac.uk/~bd512//bout
http://boutproject.github.io
22