|Dynamical Stability of Galactic Shocks: Numerical Instability
and Physical Stability
|459, 6th International Conference of Numerical Modeling of Space Plasma Flows (ASTRONUM 2011)
|Hanawa, T.; Kikuchi, D.
|We discuss the stability of hydrodynamical shock against perturbations which distort
the wave front. First we restrict ourselves to the case in which the flow is isothermal
and one-dimensional in the steady state. It is proven that such a steady shock is
stable against two-dimensional perturbations when the gas is decelerated just behind
the shock front. Next we demonstrate that the conventional numerical scheme fails to
simulate the physically stable flow when the shock is strong and the front is inclined with
the numerical cell boundary. It is also demonstrated that the numerical instability
cannot be removed by the upwind flux of the first order accuracy in space.
The instability looks quite similar to the wiggle instability appearing in the
hydrodynamical simulations of spiral galaxies. The similarity suggests that the wiggle
instability may also be of numerical origin. The numerical instability is suppressed
if we add extra numerical diffusion in the direction tangential to the shock front.
Otherwise the numerical simulation suffers from spurious vortex and excess free
energy in the post shocked flow. This instability is ascribed to the digitized error
that the shock front is not straight but zigzagged in numerical simulations.