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X. Q. Xu Lawrence Livermore National Laboratory Acknowledgement: P.W.Xi 1,2, C. H. Ma 1,2, T.Y.Xia 1,3, B.Gui 1,3, G.Q.Li 1,3, J. F. Ma 1,4, A.Dimits 1, I.Joseph 1, M.V.Umansky 1, S.S.Kim 5, T.Rhee 5, G.Y.Park 5, H.Jhang 5, P.H.Diamond 6,7, B.Dudson 8, P.B.Snyder 9 1 Lawrence Livermore National Laboratory, Livermore, California 94551, USA 2 School of Physics, Peking University, Beijing, China 3 Institute of Plasma Physics, Chinese Academy of Sciences, Hefei, China 4 Institute for fusion studies, University of Texas, Austin, TX 78712, USA 5 WCI Center for Fusion Theory, National Fusion Research Institute, Daejon, South Korea 6 CASS and Dept. of Physics, University of California, San Diego, La Jolla, CA, USA 7 University of York, Heslington, York YO10 5DD, United Kingdom 8 General 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-AC52-07NA LLNL-PRES Overview of recent BOUT++ Simulation and validation results

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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

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BOUT++ is a successor to BOUT, developed in collaboration with Univ. York* Original BOUT, tokamak applications on boundary turbulence and ELMs with encouraging results BOUT-06: code refactoring using differential operator approach, high order FD, verification BOUT++: OOP, 2D parallelization, applications to tokamak ELMs and linear plasmas X.Q. Xu and R.H. Cohen, Contrib. Plasma Phys. 38, 158 (1998) Xu, Umansky, Dudson & Snyder, CiCP, V. 4, (2008). Umansky, Xu, Dudson, et al.,, Comp. Phys. Comm. V. 180, (2008). Dudson, Umansky, Xu et al., Comp. Phys. Comm. V.180 (2009) Xu, Dudson, Snyder et al., PRL 105, (2010). Gyro-fluid extension RMPs Neutrals & impurities Preconditioner Computing on GPUs B UT++ Boundary Plasma Turbulence Code

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BOUT and BOUT++ have been products of broad international collaborations Lodestar Research Corporation Institute of plasma Physics Chinese Academy of Sciences Southwestern Institute of Physics

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BOUT++ MAP

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Principal Results 6 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 stabilization effects

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7 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 TwofluidGyrofluidPhysics Peeling-ballooning mode + acoustic wave + Thermal transport no acoustic wave + additional drift wave instabilities + Thermal transport

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A good agreement between BOUT++, ELITE and GATO for both peeling and ballooning modes As edge current increases, the difference between BOUT++ and GATO/ELITE results becomes large This difference is due to the vacuum treatment n cbm18_dens8 A D For the real “vacuum” model, the effect of resistivity should be included

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4-field model agrees well with 3-field for both ideal and resistive ballooning modes c value from eigenvalue solver agrees with BOUT simulation. Non-ideal effects are consistent in both models diamagnetic stabilization resistive mode with < c increase n of maximum growth rate with decrease of

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P. W. Xi, X.Q. Xu, P. H. Diamond, submitted to PRL, 2013

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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. Cyclone base case 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 SS Kim, et al.

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Development of flux-driven edge simulation Edge Transport Barrier formation with external sheared flow T=0 T=100 T=200 Time ExB shearing rate normalized poloidal flux SOL diffusion coefficient = – 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 normalized poloidal flux

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Six-filed simulations show that Ion perturbation has a large initial crash and electron perturbation only has turbulence spreading due to inward ExB convection TeTi

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6-field module has the capability to simulate the heat flux in divertor geometry 14 Toroidal direction (m) R (m) Inner target Outer target Outer mid-plane Six-field (ϖ, n i, T i, T e, A ||, V || ): based on Braginskii equations, the density, momentum and energy of ions and electrons are described in drift ordering [1,2]. [1]X. Q. Xu et al., Commun. Comput. Phys. 4, 949 (2008). [2]T. Y. Xia et al., Nucl. Fusion 53, (2013). Left: electron temperature perturbation Bottom: heat flux structures on toroidal direction.

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Ne (10^19 m^-3) *10^-34.03*10^-21.59*10^-13.81*10^ Collisionality at peak gradient radial position: A set of equilibrium with different density profiles are generated Pressure profile is fixed

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S=10^8, S H =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. As the edge density (collisionality) increases, the growth rate of the P-B mode increases for high n but decreases for low n (1

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SMBI particle fueling models has been implemented Physical model – plasmas, atom, molecule 18 Quasi-neutral Local Const. Flux Boundary Simulation qualitatively consistent with Expts. SMBI LCFS

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Ongoing validation of MHD instability data from EAST BOUT++ simulations show that the stripes from EAST visible camera match ELM filamentary structures Visible camera shows bright ELM structure $ BOUT++ simulation shows that the ELM stripe are filamentary structures * Z (m) Major radius R (m) $ Photo by J. H. Yang * Figure by W.H. Meyer Pitch angle match! Mode number match! T. Y. Xia, X.Q. Xu, Z. X. Liu, et al, TH/5-2Ra, 24 th IEAE FEC, San Diego, CA, USA, 2012 Z.X.Liu, et al., POSTER SESSION I

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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

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Principal Results 21 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 stabilization effects

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BOUT++ background information & websites 22 The 2013 BOUT++ workshop website, https://bout2013.llnl.gov BOUT++ background information and continuing development on the following websites: https://bout.llnl.gov

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