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

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)

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."

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.

‘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

Full Set of Fluid Equations Isotropic pressure Quasi neutrality

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

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

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

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

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.

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

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 http://csem.engin.umich.edu/

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

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

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 https://wiki.ucar.edu/display/LTR/Home

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) https://wiki.ucar.edu/display/LTR/Home Pembrook et al., 2012

Why use MHD Models?

Community Coordinated Modelling Center (CCMC) . Community Coordinated Modelling Center (CCMC) http://ccmc.gsfc.nasa.gov