1. GEM Student Tutorial: GGCM Modeling (MHD Backbone)
Jodie Barker Ream
UCLA, ESS
June 16, 2013

2. Outline Magnetohydrodynamics (MHD) General info on MHD modeling
‘Derivation’
Equations
Resistivity
General info on MHD modeling
Representative Global MHD Models
BATS-R-US
OpenGGCM/UCLA Global MHD Simulation
Lyon-Fedder-Moberry (LFM)
Community Coordinated Modeling Center (CCMC)

3. Magnetohydrodynamics
The first recorded use of the word magnetohydrodynamics is by Hannes Alfven in 1942:
"At last some remarks are made about the transfer of momentum from the Sun to the planets, which is fundamental to the theory... The importance of the magnetohydrodynamic waves in this respect are pointed out."

4. Magneto – hydro – dynamics
Dealing with magnetic and electric fields
Things change over time and space
Fluids
Magnetohydrodynamics is the study of the dynamics of electrically conducting fluids.

5. ‘Derivation’ Start with the Vlasov equation
Neglect Collisions
Take the moments description
Neglect effects of the distribution in velocity space
Look at the average properties over a given volume
Continuity Equ.
Momentum Equ.
Energy Equ.
Charge continuity
Ohm’s Law

6. Full Set of Fluid Equations
Isotropic pressure
Quasi neutrality

7. Full Set of Fluid Equations
Too many unknowns for the number of equations
How can we simplify?

8. Assumptions
Isotropic pressure
Plasma quasi-neutral
Neglect Gravity
Zero Heat Flux
Typical length scales much larger than kinetic length scales
gyro radii, skin depth, etc
Typical time scales much slower than kinetic time scales
gyro frequencies
Velocity much smaller than speed of light
Assume the resistivity due to collisionless interactions is small.
typical magnetic diffusion times must be longer than any time scale of interest.
MHD is a theory describing large scale, slow phenomena compared to kinetic theory

9. Full Set of Fluid Equations
rewrite in a quasi-conservative form

10. Ideal MHD Equations (one version)
Fluid Equations
Maxwell’s
Equations
Ohm’s Law

11. Importance of resistivity
Even in large, highly conductive systems, resistivity may still be important:
Instabilities exist that can increase the effective resistivity of the plasma substantially
Enhanced resistivity is usually the result of the formation of small scale structure like current sheets or fine scale magnetic turbulence.
One option is to use Resistive MHD.
Includes an extra term in Ohm's Law which models the anomalous resistivity.

12. Global MHD Modeling
Solve the set of MHD equations on a computational grid.
Adaptive, stretched, Cartesian, spherical, orthogonal, non-orthogonal, etc.
Boundary Conditions
Sunward outer boundary: Solar wind (ideal or measured)
Inner boundary: Ionospheric model
Each model handles the boundary conditions, grids and equations in different ways

13. BATS-R-US Numerical Method : 2nd Order solver
∇∙B=0: Numerical error in ∇∙B is controlled through the introduction of source terms proportional to ∇∙B.
Grid: adaptive mesh
Inner Boundary
Ionospheric
electrodynamics
Inner Magnetosphere
Coupled to other models through the Space Weather Modeling Framework (SWMF)
Welling and Ridley, 2010

14. UCLA Global MHD Model and OpenGGCM
Numerical Method: 4th order solver
∇∙B=0
Solar wind: shifted into a minimum variance frame with n=Const
Magnetosphere: Use a magnetic flux conservation scheme
Grid: stretched Cartesian n R
SW monitor
Raeder et al 1998, 2001; El Alaoui et al 2001

15. UCLA Global MHD Model and OpenGGCM
Numerical Method: 4th order solver
∇∙B=0
Solar wind: shifted into a minimum variance frame with n=Const
Magnetosphere: Use a magnetic flux conservation scheme
Grid: stretched Cartesian
Inner Boundary Conditions
UCLA: conductance is calculated using an emperical model based on solar EUV and discrete and diffuse precipitation from the MHD inner boundary. Coupling is done via the field aligned currents
OpenGGCM: Coupled Thermosphere Ionosphere Model (CTIM)
Raeder et al 1998, 2001; El Alaoui et al 2001

16. Lyon-Fedder-Mobarry (LFM)
Numerical Method : 8th Order solver
∇∙B=0 is obtained using a corrector algorithm
Grid: non-orthogonal stretched spherical grid
Inner boundary
MIX: Magnetosphere
Ionosphere Coupler/Solver
Lyon et al., 2004

17. Lyon-Fedder-Mobarry (LFM)
Numerical Method : 8th Order solver
∇∙B=0 is obtained using a corrector algorithm
Grid: non-orthogonal stretched spherical grid
Inner boundary
MIX: Magnetosphere
Ionosphere Coupler/Solver
Inner Magnetosphere (RCM)
Pembrook et al., 2012

18. Why use MHD Models?

19. Community Coordinated Modelling Center (CCMC).
Community Coordinated Modelling Center (CCMC)