Description
1. Basic knowledge – tutorials 1.1. Introduction to MHD simulations (solar system plasmas) 1.1. Introduction to MHD Simulations 1.1.1. MHD Equations and Properties 1.1.2. Basic Considerations for the Numerical Solution of MHD Systems 1.1.3. Initial and Boundary Conditions 1.1.4. Examples of MHD Simulations Earth’s Magnetotail Simulations Earth’s Magnetopause and Shock Simulations 1.1.5. Summary and Conclusions 1.2. Hall-MHD plasma simulation 1.2.1. Introduction 1.2.2. Hall MHD: Basic Equations and Wave Modes 1.2.1 Whistler Waves 1.2.2 Hall Drift Waves 1.2.3. Numerical Methods 1.2.3.1 Cell Definition 1.2.3.2 Time Step Scheme 1.2.3.3 Finite Volume Method 1.2.3.4 Flux Calculation 1.2.3.5 Distribution Function Method 1.2.3.6 Magnetic Field Evolution 1.2.3.7 Courant Condition 1.2.3.8 Sub-cycling the Hall Physics 1.2.3.9 Other Numerical Algorithms 1.2.4. Applications 1.2.4.1 Linear Hall Waves 1.2.4.2 Plasma Opening Switch 1.2.4.3 Magnetic Reconnection 1.2.4.4 Sub-Alfvenic Barium Clouds 1.2.5. Summary 1.3. Multi-fluid simulation 1.3.1 Introduction – state of the arts 1.3.2 Multi-fluid plasma description 1.3.3.Finite volume discretization method 1.3.4 Constraints on Maxwell equation solvers 1.3.5. Wave envelope solvers for propagation in dilute (collsionless=) plasmas 1.2.6. Adaptive mesh refinement 1.2.7 Applications – Wake field acceleration – Magnetic reconnection in relativistic plasmas 1.4. Hybrid- kinetic approach 1.4.1 Introduction a) What are hybrid codes/ Need for a hybrid model/code and why are they important? b) Summary of 2003 tutorial c) What has changed in last 15 years? d) What is the main purpose of this chapter? 1.4.2. Review of Basic Model and Implementation, Hybrid Algorithm Basics a) Basic model and equations b) Electric field advance c) Algorithm comparisons a. brief comparisons of different algorithms, numerical parameters 1.4.3. Examples of Current Applications (for each case: what is the physics being studied, why need a hybrid model, special boundary/initial conditions, diagnostics, results and their relation to observations) a) Foreshocks (Omidi) b) Planetary bow shocks: c) Magnetosheath d) Effects of shock, turbulence, reconnection (Karimabadi) e) Magnetopause reconnection (Omidi and Le) 1.4.4. Hybrid Codes in use 1.4.4.1 Current production codes a) Solar wind: i. CAM-CL algorithm ii. Hellinger – moving box iii. Franci – turbulence b) SW interaction w/ planets i. Mars (Brecht) ii. Moon (Lipatov) iii Mercury(Travnicek) c) Shocks & boundaries i. Burgess – see his own chapter ii. Gargate iii Vshivkova iv. Yu Lin d) Brief mention of finite mass hybrid codes 1.4.4.2 New hybrid algorithms: a). Kunz et al. i. Review of predictor-corrector method ii. Pegasus code for astrophysical applications, w/predictor-predictor-corrector algorithm b) Stanier et al. – implicit, energy-conserving hybrid code c) Karimabadi et al. — DES and new diagnostics separate chapters 1.4.5. The Future a) Continued interest/sims of foreshock, magnetosheath, magnetopause, magnetotail, MMS, … b) Continued interest in planetary sims: Mars, Venus, Jupiter, Mercury, Moon,…solar wind… c) In all of these cases, more interactions with observations, new diagnostics, … d. Continuing development of new computer architectures, visualization techniques, diagnostics, comparison with data…. but these areas are changing very rapidly e. Other issues In this section new hybrid code will be intrioduced and new algorithms will be discussed, the Pegasus code (M. Kunz) and energy conserving algorithms (Stanier, LANL) as well as finite electron mass hybrid codes (P. Munoz, T. Amano). The following examples will be given: large 2D foreshock cavities (N. Omidis) 3D magnetospheres (H. Karimabadi), 3D Pegasus simulations (M. Kunz). 1.5. Gyro-kinetic restricted kinetic simulation 1.5.1 Introduction: Yet another kinetic approach? 1.5.2 A primer on gyrokinetics 1.5.3 Beyond gyrokinetics 1.5.4 Computational gyrokinetics 1.5.5 Applications in space plasma physics and beyond 1.5.6 A look into the future of gyrokinetics 1.6. Eulerian Vlasov fully kinetic simulation 1.6.1 Introduction (3p) 1.6.2. Models of different Plasma Regimes (2p) 1.6.3. Initial conditions and Vlasov equilibrium (2p) 1.6.4. Numerical schemes and Hamiltonian dynamics (3p) 1.6.5. Historical overview of applications (2p) 1.6.6. Recent advancement in plasma turbulence and reconnection (3p) (or Recent advancement in space plasmas) 1.6.7. Conclusions (2p) 1.7. Particle-in-Cell fully kinetic simulation 1.7.1. From the Vlasov equation to the PiC scheme 1.7.2.Numerical implementation 1.7.2.1. field solvers 1.7.2.2. interpolation and deposition 1.7.2.3. particle motion 1.7.2.4 initialization 1.7.2.5 boundaries 1.7.2.7 diagnostics 1.7.2.7 tests 1.7.3. Technical implementation – example: the ACRONYM cod 1.7.4.Applications 1.7.4.1. transport 1.7.4.2. instabilities 1.7.4.3. shocks – see part 2 1.7.4.4. reconnection – see part 2 1.7.5.Requirements, limitations and outlook 2 Advanced simulation approaches 2.1. Adaptive Global MHD Simulations 2.1.1 Introduction 2.1.2 Brief History of Global MHD Simulations of Space Plasma 2.1.3 Early Models 2.1.3.1 Models of the Solar Corona 2.1.3.2 Heliosphere Models 2.1.3.3 Geospace Models 2.1.4 Adaptive Physics 2.1.4.1 Hydrodynamics 2.1.4.2 Ideal and Resistive MHD 2.1.4.3 Hall MHD 2.1.4.4 Multispecies and Multifluid MHD 2.1.4.5 Moment Closure Without Ohm’s Law 2.1.5 Framework, Codes and Model Coupling 2.1.5.1 SWMF 2.1.5.2 BATS-R-US 2.1.5.3 MHD-EPIC 2.1.6 Solar-Heliosphere Modeling: AWSOM 2.1.7 Magnetosphere Modeling 2.1.8 Planetary Applications 2.2. Mesoscale HD and MHD simulations of the Interstellar Medium in Galaxies 2.2.1. Introduction 2.2.2. ISM Modelling: Problems and Tasks a) Supernova Driven Compressible Turbulence b) The Role of the Galactic Fountain c) The Role of the Magnetic Fields and Cosmic rays 2.2.3. Three-dimensional High Resolution HD and MHD simulations a) Numerical Setup b) Adaptive Mesh Refinement c) Parallel Computing 2.2.4. The Importance of Coupling the Ionization Structure to the Dynamics a) Atomic Data and Timescales b) Deviations from Maxwellian Distributions c) Time-Dependent Emissivity 2.2.5. Results a) Structure and Evolution of the ISM b) Distribution of Ionized Species c) Galactic Outflow and Mass loss d) Simulation of the Local ISM 2.3. Coupling of Kinetic and MHD simulations Giovanni Lapenta at al. 2.4.1 Use of implicit and semi implicit PIC to cover moultiple scales – implicit moment method – sem-implicit – fully implicit 2.4.2 grid adaptation – adaptive grids – AMR and MLMD 2.4.3 fluid-kinetic coupling – use of different approaches – one way – two way 2.4.4 Example of application – dayside – tail – full planetary models – coalescence – turbulence 2.4. Shock waves in space plasma 2.3.1 Introduction 2.3.1.1. The key role of shocks in space plasmas – range of observed shocks – shocks in fluid dynamics – near-discontinuous solutions – collisionless plasma shocks and shock parameters – the main problem: dissipation without collisions – importance of particle kinetics, instabilities and waves – the main aim of simulations: shock structure: how it arises & what it does – applications of shock simulations: particle acceleration, global systems 2.3.2. Scales and simulations – some of typical scale sizes in shocks (from Debye to global systems) – cross-scale coupling in shocks – use of different simulation methods – resolution and computational constraints – choosing the appropriate simulation method – full particle PIC (resolving electron scales) – hybrid – test particle plus MHD (for particle acceleration) – Vlasov (plus discussion relative merits compared with PIC) – How to form a shock in a simulation – methods and examples (using hybrid) – discussion of advantages, issues, time scales, etc. – initialization from jump conditions – creation by piston: inflow plus wall 2.3.3. Shock simulation and particle acceleration – examples of shock simulations with general astrophysical application – some numerical issues to be considered – ion acceleration at quasi-parallel shocks (hybrid) – electron acceleration – full PIC simulations 2.3.4. Summary – summary, outlook and future challenges 2.5. Magnetic reconnection in space plasmas This section will try to explain what features of reconnection and their consequences can be modeled with the most common plasma models, including but not limited to fully-kinetic, hybrid-kinetic, gyrokinetics, two-fluid, EMHD, Hall-MHD and MHD. It will try to be a guide for the correct choice of plasma model and its associated numerical codes depending on the reconnection physics intended to be investigated. In addition, this section will also review the most recent findings obtained with numerical simulations. 2.5.1: The parameter space of magnetic reconnection. – phase diagram – the role of collisionality 2.5.2: Balance of the reconnection electric field – Generalized Ohm’s law – Balance by pressure-term: plasma models including electron non gyrotropy – Balance by the inertia term: From PIC, inertial hybrid-PIC to EMHD – Resistive reconnection: Hybrid and MHD reconnection – Anomalous-resistivity: what kind of fluctuations are allowed in each model? Numerical evidence in favour/against. 2.5.3: Physics of the diffusion region – Electron and ion diffusion regions: two-fluid effects. – Egedal model: the role of the anisotropy on the structure of the diffusion region 2.5.4: Heating and acceleration mechanisms – Models including CGL physics – Betatron acceleration – Pickup processes: hybrid codes – Fermi-acceleration at electron and ion scales. Test-particle approach. – Turbulent heating/resonant processes in fully-kinetic. 2.5.5: The role of plasma-beta and guide fields – The strong-guide field limit: GK models – low-beta limit: reconnection in extended MHD models, gyrofluid. 2.5.6: Waves in reconnection – KAW physics: Hybrid and extended MHD models – Whistler wave physics: EMHD 2.5.7: Current sheet instabilities – Electron beam instabilities and other electron micro-instabilities (two-streaming, Langmuir wave emission, radio emission): PIC – Ion beam instabilities: Hybrid. – Lower-hybrid instabilities: Role of pressure gradients – Temperature anisotropy instabilities: the role of mirror and firehose instabilities in the exhaust of reconnection (PIC vs hybrid). – Shear flow instabilities: KH in MHD vs electron K-H in EMHD 2.5.8: Eulerian vs Lagrangian methods: – Thermal vs numerical noise. – The advantages of Eulerian/Vlasov approaches. 2.5.9: Summary and outlook – future directions 3. New algorithms and developments for future simulations 3.1. Higher-order numerical solutions of the continuum MHD equations Introduction 2. General numerical framework 3.1.2.1 System of equations to be solved 2.2 Motivation for using higher-order schemes 2.3 Finite-Volume 2.4 Constrained Transport 3. Practical Computation of the Fluxes 3.1 Central Weighted Essentially Non Oscillatory reconstruction 3.2 Reconstruction of the magnetic field components 3.3 Solving the Riemann problem 3.4 Passage through point values 3.5 Electric fluxes on the edges 3.6 Summary: the complete procedure to determine the R.H.S. 4. Time integration 5. Strong shocks and negative pressure/density 6. Numerical tests 6.1 Verfication of the scheme’s order 6.2 Smooth problems 6.2.1 Circularly polarized Alfv_en wave 6.2.2 3D MHD vortex 6.3 Shocked problems 6.3.1 1D Brio-Wu Riemann problem 6.3.2 Orszag-Tang vortex 6.3.3 Decaying supersonic MHD turbulence 7 Final remarks 3.2. Self-Adaptive algorithms for multiscale simulations – the discrete event technology 1. Introduction 1.1.Time vs change 1.2. Multiple stepping techniques: bottlenecks 1.3. Discrete Event Simulation (DES): updates as events 2. EMAPS: Event-driven Multiscale Asynchronous Parallel Simulation 2.1 . Early serial algorithms: 1D diffusion-advection-reaction, hybrid 2.2 Parallel EMAPS: Preemptive Event Processing, 1D CFD 2.3 HYPERS: HYbrid Parallel Event-Resolved Simulator (2D/3D) code 2.4 Latest advances in HYPERS: separate event queues for particles and fields, magnetic field correction, boundary conditions, resistivity models . 3. HYPERS Applications 3.1. Global magnetospheric simulation, 2D and 3D 3.2. 2D examples > 820x1640x1640 cells) 3.4. Applications inspired by EMAPS 3.5. Discharge modeling 3.6. Oil and reservoir modeling 3.7. Fire propagation, CFD 4. Future applications 4.1. Hybrid plasma modeling: “on-demand” particle and field algorithms, dynamic load balancing, hybrid (MPI/OpenMP) parallelization, cut cells for modeling plasmas 4.2. Magnetospheric physics: expanding the size and physics of global simulations, coupling global simulations with inner magnetosphere models 4.3. Radiation belts and reconnection (XHYPERS) 3.3. Techniques for effective scientific visualization and discovery including illustrative examples from petascale simulation results 3.3.1. Introduction 1.1. Pathlines, streaklines, streamlines 1.2. Intelligent contouring 1.3. Topology maps 1.4. FTLE 1.5. In situ visualization 1.6. Development of techniques that led to major scientific discovery 3.3.2. Discovering and visualization of flow patterns (field lines, pathlines) 2.1. Parallel algorithms for flow patterns 2.2. Applications to global simulations 3.3.3 Intelligent Contouring: Line Integral Convolution (LIC) 3.1. 2D 3.2. 3D 3.3. Examples to reconnection and global simulations 3.3.4. Topology Map 4.1. Description of the algorithm 4.2. Example demonstration for finding and tracking field lines in 3D global simulations 3.3.5. FTLE.
