GEM 2002 Student Tutorial Global MHD Simulation in

GEM 2002 Student Tutorial Global MHD Simulation in Geospace Yongli Wang IGPP/UCLA Special Thanks to Dr. J. Raeder for his help to prepare the material 1/31/2022 2002 GEM Student Tutorial 1

Outline Introduction to the Global MHD Simulation n How to perform global MHD Simulation n New Techniques and Challenges n 1/31/2022 2002 GEM Student Tutorial 2

ser Ob Synthesis ies eor va Th tio ns What Make Up the Space Physics? Simulations 1/31/2022 2002 GEM Student Tutorial 3

Properties of Numerical Solution Methods n Why we use simulations: – – – – n Put spacecraft into context. Parameter dependence study; Boundary conditions; Temporal dependence study; Nonlinear problems; Unobserved regions Complex geometry A robust simulation has the following properties: [J. H. Ferziger and M. Peric, Computational Methods for Fluid Dynamics, Springer, 1999] ü Consistency ü Boundedness ü Stability ü Realizability ü Convergence ü Accuracy ü Conservation 1/31/2022 2002 GEM Student Tutorial 4

What is the Global MHD Simulation Global MHD simulation is the numerical simulation of the geospace environment with MHD equations as the governing equations. 1/31/2022 2002 GEM Student Tutorial 5

History of Global MHD Simulation n n n 1978: First 2 d simulations by Leboeuf et al. Early 1980’s: First 3 d simulations (Brecht, Lyon, Wu, Ogino). Late 1980’s: Model refinements (FACs, ionosphere, higher resolution, fewer symmetries). Early 1990’s: Long geomagnetic tails, refined ionosphere models. Mid 1990’s: First comparisons with in situ observations. Beginning of quantitative modeling. Late 1990’s: Global models become an integrated part of many experimental studies and models provide extension to observations and theoretical studies. Early 2000’s: Global models begin to be accessible for the whole community. Improved boundary conditions. 1/31/2022 2002 GEM Student Tutorial 6

MHD Theory and Equations n The basis of MHD: – Vlasov-Boltzman Equation – Maxwellian Equations n Some fundamental requirements for MHD – Debye Length and ND – Scale length is larger than ion gyro-radius and time scale should be larger than gyroperiod. – Localization 1/31/2022 2002 GEM Student Tutorial 7

Grids 1/31/2022 2002 GEM Student Tutorial 8

Initial Condition n Criteria for initial condition: – Final configuration has no dependence on the initial condition – Small time to reach realistic configuration n Example 1/31/2022 2002 GEM Student Tutorial 9

Boundary Condition n Outer boundary: – Observational solar wind input – Idealized solar wind input – Input from solar wind models n Inner boundary: – Ionosphere; inner magnetosphere (Ring current) – Mapping; continuous 1/31/2022 2002 GEM Student Tutorial 10

Algorithms n Integration: – Spatial integration » Finite difference method » Finite volume method » Finite element method – Temporal integration » Multiple step method (predictor-corrector method) » Runge-Kutta method n Time step determination: CFL condition [J. H. Ferziger and M. Peric, Computational Methods for Fluid Dynamics, Springer, 1999 ] 1/31/2022 2002 GEM Student Tutorial 11

Parallelization n MPI (Message Passing Interface) – Designed for high performance on both massively parallel machines and on workstation clusters – Widely available: free or vendor supported. – Cross platform – Multiple language: Fortran, C/C++, … n Parallel computation facilities: – Massively parallel machines: CRAY-T 3 E, IBM-SP 2, SGI-ORGIGIN 2000, … – Workstation clusters : PC Beowulf clusters, … 1/31/2022 2002 GEM Student Tutorial 12

A Super Computer Example: IBM Bluehorizon 1/31/2022 2002 GEM Student Tutorial 13

Beowulf in My Office 1/31/2022 2002 GEM Student Tutorial 14

Fundamental Difficulties in MHD Simulation n n How to Determine Resistivity Progress in the field of computer fluid dynamics. however, there are extra difficulties for MHD – Much More complex MHD than Fluid – Divergence of B free – Special characteristics that MHD equations show compared to the simpler fluid equations. 1/31/2022 2002 GEM Student Tutorial 15

Current Major Global MHD Models Dartmouth/NRL/Maryland LFM (J. Lyon, J. A. Fedder, C. Mobarry) n GEDAS (Japan, T. Ogino) n ISM (G. L. Siscoe) n Michigan BATS-R-US (T. I. Gombosi) n UCLA (J. Raeder) n U. of Washington (R. M. Winglee) n…… n 1/31/2022 2002 GEM Student Tutorial 16

Outline Introduction to the Global MHD Simulation n How to perform global MHD Simulation n New Techniques and Challenges n 1/31/2022 2002 GEM Student Tutorial 17

Can a Non-Modeler Do Global Simulation? n Models are readily available for community use: – CCMC: http: //ccmc. gsfc. nasa. gov/ – UCLA: http: //www-ggcm 2. igpp. ucla. edu/ n Source codes in public domain: – GEDAS (Japan, T. Ogino) http: //gedas 22. stelab. nagoya -u. ac. jp/simulation/jst 2 k/hpf 02. html – BATSRUS: http: //csem. engin. umich. edu/ – NRL: http: //www. lcp. nrl. navy. mil/hpcc-ess/software. html » FCTMHD 3 D (C. R. De. Vore) » AMRMHD 3 D (P. Mac. Neice) – Zeus 3 D MHD (Michael Norman): http: //zeus. ncsa. uiuc. edu: 8080/lca_intro_zeus 3 d. html – CDF Codes: http: //icemcfd. com/cfd/CFD_codes. html 1/31/2022 2002 GEM Student Tutorial 18

How to Make Global MHD Simulation What do you want to solve? Why do you want to use global model? What results do you expect from a global model? Set model parameters and provide necessary input files Run global model Analyze model results Possible combination with other results (theory, observation) Ready for publication? 1/31/2022 2002 GEM Student Tutorial 19

What Can We Do with Global MHD Model? n n n Space Weather Magnetosphere dynamics (storm, substorm, magnetotail configuration) Bow shock and magnetosheath dynamics Solar wind-magnetosphere interaction M-I coupling. More reference can be found: http: //pallas. igpp. ucla. edu/jraeder/ http: //ccmc. gsfc. nasa. gov/ 1/31/2022 2002 GEM Student Tutorial 20

How to Make Global MHD Simulation What do you want to solve? Why do you want to use global model? What results do you expect from a global model? Set model parameters and provide necessary input files Run global model Analyze model results Possible combination with other results (theory, observation) Ready for publication? 1/31/2022 2002 GEM Student Tutorial 21

Model parameters and solar wind input n Parameters in the model: – – – Computation domain settings (Simulation box size, grid settings) Boundary condition (e. g. , inner boundary location, boundary type) Ionosphere conductivity (constant conductivity, empirical conductivity model, ionosphere model) – Resistivity parameters – Simulation run time – Data output control parameters (output frequency, output data location and type) – Debugging parameters (debugging message output) Click to see a sample parameter input for global MHD model. n Solar wind inputs: – Idealized (constant, staggered, jumped, …) – Realistic (usually solar wind plasma and IMF 1/31/2022 observations) 2002 GEM Student Tutorial 22

Example of Idealized Solar Wind Input 1/31/2022 2002 GEM Student Tutorial 23

Example of Realistic Solar Wind Input 1/31/2022 2002 GEM Student Tutorial 24

How to Make Global MHD Simulation What do you want to solve? Why do you want to use global model? What results do you expect from a global model? Set model parameters and provide necessary input files Run global model Analyze model results Possible combination with other results (theory, observation) Ready for publication? 1/31/2022 2002 GEM Student Tutorial 25

Visualization 1/31/2022 2002 GEM Student Tutorial 26

Parameter Study 1/31/2022 2002 GEM Student Tutorial 27

Comparison with Observations Solar wind and magnetosphere in situ observations 1/31/2022 Comparison between model and in situ observations 2002 GEM Student Tutorial 28

How to Make Global MHD Simulation What do you want to solve? Why do you want to use global model? What results do you expect from a global model? Set model parameters and provide necessary input files Run global model Analyze model results Possible combination with other results (theory, observation) Ready for publication? 1/31/2022 2002 GEM Student Tutorial 29

Publications 1/31/2022 2002 GEM Student Tutorial 30

Outline Introduction to the Global MHD Simulation n How to perform global MHD Simulation n New Techniques and Challenges n 1/31/2022 2002 GEM Student Tutorial 31

Adaptive Mesh Refinement (AMR) Standard Shock Tube Problem 1/31/2022 N=100 Grids 2002 GEM Student Tutorial N=1000 Grids 32

AMR (continued) 1/31/2022 2002 GEM Student Tutorial 33

A Movie Showing a Simulation with AMR Click to play the movie! 1/31/2022 2002 GEM Student Tutorial 34

Data Assimilation with Multi-spacecraft Observations 1/31/2022 2002 GEM Student Tutorial 35

Multi-Scale Simulation 1/31/2022 2002 GEM Student Tutorial 36

Other Difficulties and Fronts n Coupling with models with other space regions (even with different physics) – Inward: » Atmosphere, ionosphere and thermosphere models » Ring current and radiation belt models – Outward: » Solar wind models n Difficulties with realistic solar wind inputs – Solar wind Bx problem n n Global simulation other than MHD Simulation with direct coupling of different types of simulations. 1/31/2022 2002 GEM Student Tutorial 37

The Ends 1/31/2022 2002 GEM Student Tutorial 38