Space Weather Prediction: Challenges in Computational Magnetohydrodynamics. Gábor Tóth Center for Space Environment Modeling University of Michigan. Collaborators. Tamas Gombosi, Kenneth Powell Ward Manchester, Ilia Roussev Darren De Zeeuw , Igor Sokolov Aaron Ridley, Kenneth Hansen
DoD MURI and NASA CT Projects
Conditions on the Sun and in the solar wind, magnetosphere, ionosphere, and thermosphere that can influence the performance and reliability of space-born and ground-based technological systems and can endanger human life or health.
Space physics that affects us.
Conservative form is required for correct jump conditions across shock waves.
Energy conservation provides proper amount of Joule heating for reconnection even in ideal MHD.
Non-conservative pressure equation is preferred for maintaining positivity.
Hybrid scheme: use pressure equation where possible.MHD Equations in Conservative vs. Non-Conservative Form
Large truncation errors.
Pressure calculated from total energy can become negative.
Difficult to maintain boundary conditions.
Solution: split the magnetic field as B = B0 + B1 where B0 is a divergence and curl free analytic function.
Gradients in B1 are small.
Total energy containsB1 only.
Boundary condition for B1 is simple.Splitting the Magnetic Field
Blocks communicate with neighbors through “ghost” cells
Each block is NxNxN
The Sun-Earth system consists of many different interconnecting domains that are independently modeled.
Each physics domain model is a separate application, which has its own optimal mathematical and numerical representation.
Our goal is to integrate models into a flexible software framework.
The framework incorporates physics models with minimal changes.
The framework can be extended with new components.
The performance of a well designed framework can supercede monolithic codes or ad hoc couplings of models.From Codes To Framework
Solar Corona interconnecting domains that are SCBATSRUS
Eruptive Event GeneratorEEBATSRUS
Inner HeliosphereIH BATSRUS
Solar Energetic ParticlesSPKóta’s SEP model
Global Magnetosphere GM BATSRUS
Inner MagnetosphereIM Rice Convection Model
Ionosphere ElectrodynamicsIERidley’s potential solver
Upper AtmosphereUA General Ionosphere Thermosphere Model (GITM)Physics DomainsID Models
LAYOUT.in for 20 PE-s
ID ROOT LAST STRIDE
SC 0 9 1
IH 0 9 1
GM 10 17 1
IE 18 19 1
IM 19 19 1
Stream line and field line tracing is a common problem in space physics. Two examples:
Coupling inner and global magnetosphere models
Coupling solar energetic particle model with MHD
Tracing a line is an inherently serial procedure
Tracing many lines can be parallelized,but
Vector field may be distributed over many PE-s
Collecting the vector field onto one PE may be too slow and it requires a lot of memoryParallel Field Line Tracing
needs the field line volumes,
average pressure and density
along field lines connected to
the 2D grid on the ionosphere.
Global magnetosphere model:
needs the pressure correction
along the closed field lines:
1. Trace lines inside blocks
starting from faces.
2. Interpolate and
3. Repeat 2. until the mapping
is obtained for all faces.
4. Trace lines inside blocks
starting from cell centers.
5. Interpolate mapping to
4. space physics. Two examples: Receive lines from other PE-s.
5. If received line go to 2a.Parallel Algorithm without Interpolation
1.Find next local field line.
2. If there is a local field line then
2a. Integrate in local domain.
2b. If not done send to other PE.
3. Go to 1. unless time to receive.
6. Go to 1. unless all finished.
Pressure and magnetic field
Density and magnetic field
at shock arrival time
South Turning BZ
North Turning BZ
Before shock hits. space physics. Two examples:
After shock: currents and the resulting electric potential increase.
Region-2 currents develop.
Although region-1 currents are strong, the potential decreases due to the shielding effect.
Current PotentialIonosphere Electrodynamics
The Hall conductance is calculated by the Upper Atmosphere component and it is used by the Ionosphere Electrodynamics.
After the shock hits the conductance increases in the polar regions due to the electron precipitation.
Note that the conductance caused by solar illumination at low latitudes does not change significantly.
Before shock arrivalUpper Atmosphere
After shock arrival