-
Existence of intermediate MHD shocks
proven in 3D simulations
Magnetohydrodynamics (MHD) describes the dynamical
evolution of a conducting fluid or plasma. The MHD equations are used in
solar and space physics, and in laboratory plasma physics (e.g. nuclear
fusion
in Tokamaks). The MHD equations are nonlinear
and allow for the formation of shocks (think about the sonic boom).
There are three kinds of shocks in MHD plasmas.
One of these three types, the intermediate shock type, was believed to
be unstable until recently. I have shown in 3D simulations that intermediate
shocks can naturally occur in MHD flows, and that they are stable when
perturbations are not too large. This is in accordance with recent analytical
results on the stability of intermediate shocks when dissipation is finite.
Intermediate shocks have only seldomly been observed,
but maybe the CLUSTER II mission will find some in the Earth's bow shock
soon.
About intermediate shocks in general:
`Overcompressive shocks and compound shocks in 2D and
3D magnetohydrodynamic flows' [pdf]
H. De Sterck and S. Poedts
Proceedings of the Eighth International Conference on
Hyperbolic Problems: Theory, Numerics, Applications, Magdeburg,
2001 (invited talk)
About intermediate shocks in 3D MHD flows:
`Intermediate shocks in three-dimensional magnetohydrodynamic
bow shock flows with multiple interacting shock fronts'
[pdf]
H. De Sterck and S. Poedts
Phys. Rev. Lett. 84 (24),5524, 2000
About the stability of intermediate shocks and
their role in Space Physics:
`Disintegration and reformation of intermediate shock
segments in three-dimensional MHD bow shock flows'
[pdf]
H. De Sterck and S. Poedts
J. Geophys. Res. 106, 30,023, 2001
-
Multi-dimensional Upwind Constrained
Transport (MUCT) of divergence-free fields on unstructured grids
I have developed novel algorithms for the numerical
simulation of the transport of divergence-free vector fields on unstructured
grids. Constrained Transport (CT) schemes conserve the divergence-free
nature of the vector fields up to machine accuracy. They were known on
unstructured grids. Multi-dimensional Upwind (MU) schemes discretize hyperbolic
systems on unstructured grids taking into account the wave propagation
in a truly multi-dimensional fashion. In the new MUCT schemes, the concept
of Constrained Transport, generalized to unstructured triangular grids
using `edge elements' and `face elements', is combined with the concept
of Multi-dimensional Upwind schemes. This results in fully upwind schemes
that conserve the divergence-free nature of vector fields up to machine
accuracy on unstructured grids.
The paper about the MUCT schemes:
`Multi-Dimensional Upwind Constrained Transport on Unstructured
Grids for Shallow Water Magnetohydrodynamics'
[pdf]
H. De Sterck
AIAA Paper 2001-2623, 2001