Numerical heat conduction in hydrodynamical models of colliding hypersonic flows

TL;DR

This paper investigates how numerical conduction and viscosity affect the dynamics and X-ray emission in hydrodynamical models of colliding hypersonic flows, emphasizing the importance of resolution and numerical effects.

Contribution

It systematically analyzes the impact of numerical conduction and viscosity on simulated shock dynamics and emission, providing insights for more accurate astrophysical modeling.

Findings

Numerical conduction causes erroneous heating across contact discontinuities.

Increased numerical viscosity dampens instabilities and can re-heat gas via sub-shocks.

Higher resolution reduces numerical conduction effects.

Abstract

Hydrodynamical models of colliding hypersonic flows are presented which explore the dependence of the resulting dynamics and the characteristics of the derived X-ray emission on numerical conduction and viscosity. For the purpose of our investigation we present models of colliding flow with plane-parallel and cylindrical divergence. Numerical conduction causes erroneous heating of gas across the contact discontinuity which has implications for the rate at which the gas cools. We find that the dynamics of the shocked gas and the resulting X-ray emission are strongly dependent on the contrast in the density and temperature either side of the contact discontinuity, these effects being strongest where the postshock gas of one flow behaves quasi-adiabatically while the postshock gas of the other flow is strongly radiative. Introducing additional numerical viscosity into the simulations has the effect of damping the growth of instabilities, which in some cases act to increase the volume of shocked gas and can re-heat gas via sub-shocks as it flows downstream. The resulting reduction in the surface area between adjacent flows, and therefore of the amount of numerical conduction, leads to a commensurate reduction in spurious X-ray emission, though the dynamics of the collision are compromised. The simulation resolution also affects the degree of numerical conduction. A finer resolution better resolves the interfaces of high density and temperature contrast and although numerical conduction still exists the volume of affected gas is considerably reduced. However, since it is not always practical to increase the resolution, it is imperative that the degree of numerical conduction is understood so that inaccurate interpretations can be avoided. This work has implications for the dynamics and emission from astrophysical phenomena which involve high Mach number shocks.