Numerical Bow Shock Instabilities in Inert Polyatomic Gases

TL;DR

This paper studies numerical instabilities in simulations of hypersonic flow over a sphere in inert polyatomic gases, highlighting the importance of mesh resolution and gas properties in avoiding artifacts.

Contribution

It identifies and characterizes a new type of numerical instability in hypersonic flow simulations involving inert polyatomic gases with low specific heat ratios.

Findings

Numerical instabilities can develop near stagnation points in coarse mesh simulations.

These instabilities resemble physical bow shock oscillations observed experimentally.

Inert gases with low gamma can cause numerical artifacts mistaken for real phenomena.

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 ($\gamma \approx 1.1$--$1.2$). 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 $\gamma$, our results emphasize the need for caution to avoid conflating genuine physical instabilities with numerical artifacts in simulations.