Report

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 (, , ∥ ) ( , , ∥ ) Peeling-ballooning mode 4-field 2+0 (, , ∥ , ∥ ) ( , , ∥ , ∥ ) 5-field + Thermal transport no acoustic wave , , ∥ , , 6-field , , ∥ , ∥ , , Braginskii equations + acoustic wave 3+1 ( , , ∥ , ∥ , ⊥ , ∥ , ) 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 > is shifted to > 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 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) [email protected] 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