Numerical Bow Shock Instabilities in Inert Polyatomic Gases

Abstract

We investigate inviscid numerical instabilities that arise in simulations of axisymmetric flow over a hypersonic sphere in an inert, calorically perfect gas at low specific heat ratio ($γ\approx 1.1$--$1.2$). We show that when the density ratio across the bow shock is high and the computational mesh is relatively coarse, numerically induced traveling-wave instabilities of the carbuncle type can develop in the shock layer near stagnation for inert gases. These instabilities, not previously documented in the literature, are noteworthy because bow shock oscillations are also observed experimentally in polyatomic gases exhibiting post-shock thermochemical relaxation. When such gases are modeled as inert with an effectively low $γ$, our results emphasize the need for caution to avoid conflating genuine physical instabilities with numerical artifacts in simulations.

Figures (4)

• Figure 1: (a) Axisymmetric computational domain. (b) Instantaneous density fields for two different examples that exhibit shock-layer corrugations.
• Figure 2: Effect of the eigenvalue limiter parameter $\varepsilon$ on the shock-layer instability. Top row shows instantaneous density $\rho$; bottom row shows wall-normal density gradient $\partial\rho/\partial y$.
• Figure 3: RMS density perturbation amplitude $|\rho'_\mathrm{rms}|$ as a function of eigenvalue limiter parameter $\varepsilon$ for two grid spacings ($\Delta_s = 0.1$ and $\Delta_s = 0.05$).
• Figure 4: Spatial structure of the instability for two cases ($\Delta_s=0.1$, $\varepsilon=0.3$) and ($\Delta_s=0.05$, $\varepsilon=0.2$): (a) instantaneous density $\rho$ and (b) density perturbation $\rho'$ of the dominant SPOD mode.