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1998 GEM Snowmass Workshop Reports
GGCM Campaign: Global MHD  
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From: Frank Toffoletto (toffo@rice.edu)

Several representatives from the Global MHD community were asked to 
present details of the inner workings of their respective codes. 
Four presentations were made at the 1998 GEM Snowmass meeting.

The first presentation was by Kenneth Powell from the University of 
Michigan who described the "BATS-R-US" (Block-Adaptive Tree 
Solar-Wind Upwind Roe-Type Upwind Scheme) MHD code.  This approach 
uses is an adaptation of the approximate Riemann schemes that are 
popular in computational fluid dynamics.  Riemann solvers have the 
advantage of satisfying the Rankine-Hugoniot conditions exactly, have 
the lowest possible dissipation, and are robust across a wide range 
of plasma-betas; disadvantages are that the scheme requires more 
computation per iteration and any change in the physical model 
requires some effort in computing the eigensystem.  Powell also 
outlined the adaptive mesh refinement (AMR) technology that has been 
utilized in the Michigan code, which allows dynamic changes in grid 
resolution as necessary.  He also described the method used to ensure 
that the divergence of the magnetic field is kept small; the approach 
is to modify the MHD equations to include a source term that is 
proportional to the divergence of B which has the effect of the 
passively convecting any magnetic divergence out of the system.

The second presentation was by John Lyon of Darmouth College who 
described the numerical techniques used in Fedder-Lyon-Mobarry Global 
MHD code, which was originally developed at the Naval Research 
Laboratory.  The code uses a finite volume scheme with high order 
spatial differencing on an adapted curvilinear grid.  While the 
curvilinear grid requires the computation of metrics, its inherent 
structure allows the grid to be adapted to best suit the problem. 
Lyon discussed the philosophy behind the total variation diminishing 
(TVD) scheme that is used in his code, which employs non-linear 
numerical switches based on the Partial Donor method.  He also 
described the technique of keeping the magnetic field on the cell 
faces and the electric field on the edges to ensure a zero divergence 
of the magnetic field (Yee grid).  In addition, he also outlined the 
importance of additional physical models, such as a realistic 
ionosphere model and model for parallel potential drops that are 
necessary in any global magnetosphere model.

Bill White described the Global MHD code ISM (Integrated 
Space-Weather-Prediction Model) that is under development at the 
Mission Research Corporation.  The code uses a two fluid description 
consisting of an ion plasma and a neutral fluid.  The calculations 
are carried down into the ionosphere on a two-grid system: an inner 
Earth-centered grid and an outer cylindrical grid.  Details of the 
equations solved that also include chemistry were presented.

Joachim Raeder of UCLA gave a "Nuts and Bolts" overview of what 
requirements and components are necessary to build a physically 
reasonable MHD-based model of the magnetosphere.  He described the 
model equations and the various components that have been added to 
his code to augment MHD including the ionosphere and the resistivity 
models.  The presentation focussed on several numerical issues such 
as the advantages and disadvantages of various grid schemes, dealing 
with initial and boundary conditions, the difficulties of solving the 
MHD equations and the various approaches that have been used, 
techniques for maintaining the divergence of the magnetic field zero 
and model validation.  He also outlined the computational issues that 
must be dealt with if a code is to run on modern massively parallel 
computers.  Copies of this presentation can be found at 
http://pallas.igpp.ucla.edu/jraeder/pub/paper_006.pdf.