Staff report

S. Bingert

3D MHD Solar Corona Models

temporal evolution roughly the same

both show fine and blurred structures

H. Peter; S. B.

MHD equations for an ideal gas

I) Conservation of mass

II) Conservation of momentum

III) Energy balance

IV) Induction equation

Equation of state

Eq. of state to correlate pressure with temperature

gas constant

mean atomic weight

Mean atomic usually not constant in space !

What is the effect on our coronal models?

Experiments

we did 11 experiments:

varying mean atomic weight from 0.5 to 1 in steps of 0.05

using ionization of hydrogen (+ fixed neutral helium component)

small mu

large mu

Hydrogen ionization

mean atomic weight large

at the bottom layer and

small at the top

almost step function

Hydrostatic equilibrium

density (pressure) scale height sensitive to mu at low

temperatures

Same Corona as every time

radiative loss are proportional to density squared

temperature rises

density scale height increases

smaller mu increases scale height even more but not visible

Current work

Three numerical experiments

MDI/Soho August 2002

1283 grid points

400 km resolution

Not time dependent

scaled down

HMI/SDO August 2010

2563 and 5123 grid points

400 km and 200 km resolution

time series of 6h

not scaled

small active region

Goals:

longer time series (before 2h)

changing total absolute magnetic flux emission?

finding the “blob” again? Or other features?

New equations

small uses regular code

large use Non-Fourier heat conduction

Fick’s first law non-Fickian diffusion

Fourier law non-Fourier heat conduction

Time dependent heat flux vector is known

from 8th moment approximation of the kinetic equations

Weak scaling

Scaling ~

1/ncpus0.88

• Three different problem

sizes

• scaling is not ideal

• good for the selected

number of cores

• Speed of a single cpu

• Comparison between architectures

• Code should be optimized for one

core first

HMI/SDO

Use observed HMI time series as input

HMI/SDO large

to cold

but wide spread

and strong gradients

very low density

due to missing heating

steep gradient

and good spread

max

min

horizontal average

HMI/SDO small and large

simplified doppler velocity

weighted with density

squared

missing blue shifts

units are fine

units are fine

to cold

maximum at logT=6

Doppler velocity derived from u and rho

Dem derived from T and rho

large average small average

small last large last

HMI/SDO small

Synthesized AIA 304 emission using the response function

Future work OLD

Coronal extension of a high resolution flux emergence

simulation by Mark Cheung:

• data arrived

• converting to proper input data

Solar atmosphere above HMI/SDO magnetic field time series:

• running at the GWDG

Including simple low resolution convection to compute

self consistently the magnetic field evolution at the

solar surface

• Convection works in 2D and 3D

• Dynamo process observed in these models

Future Work NEW

Including simple low resolution convection to compute

self consistently the magnetic field evolution at the

solar surface

• Convection works in 2D and 3D

• Dynamo process observed in these models

Analyze the data of the HMI/SDO experiments

Rerun small experiment with different magnetic flux