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Paper: Dynamical Stability of Galactic Shocks: Numerical Instability and Physical Stability
Volume: 459, 6th International Conference of Numerical Modeling of Space Plasma Flows (ASTRONUM 2011)
Page: 310
Authors: Hanawa, T.; Kikuchi, D.
Abstract: 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.
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