### Project A2

**Principal Investigator:**

*Rainer Grauer, Theoretical Physics I, Ruhr-University Bochum*

**Main Collaborators in the Research Unit:**

*Gregor Gassner, Department of Mathematics and Computer Science,
University of Cologne*

*Manuel Torrilhon, Applied and Computational Mathematics, RWTH Aachen*

*Eric Sonnendrücker, Computational Plasma Physics, IPP MPI & TU Munich*

## Coupling the two-fluid/Maxwell system to Magnetohydrodynamics/Ohm's law

Astrophysical and space plasmas can be considered to be collisionless. The
spatial and temporal scales occurring in such plasmas span more than 7 orders of
magnitude from the finest kinetic to the global scales. Therefore, a
multiscale/multiphysics modelling of plasmas is essential.

In this project we consider the surface coupling of the two-fluid/Maxwell with
the magneto-hydrodynamic (MHD) description. The transition from the
two-fluid/maxwell to the MHD description contains several singular limits: i)
the speed of light tends to infinity, ii) the ratio of Debye to system length
vanishes and the electron mass is neglected. This leads to interesting questions
when coupling MHD to the two-fluid/Maxwell system, such as: i) How can the
information missing in the MHD be "reconstructed" to define consistent fluxes at
the boundaries of the two descriptions? ii) How can a consistent energy density
be formulated? iii) How can refinement criteria be defined to indicate when the
MHD description is no longer appropriate?

All these questions will be addressed in project A2.

**Detailed description**

Electro-Chemistry
Extended-version