On the grid dependence of hydrodynamic stability analysis in solid rocket motors

In this numerical study, we investigate the grid dependence of the Chebyshev collocation algorithm for flow stability analysis of solid rocket motors. Conventional analyses tend to focus on how the errors of the individual eigenvalues depend on the level of grid refinement. Here, we perform a structural error analysis to estimate the overall error of the computed spectrum. First, we validate the structural error analysis on a structural oscillation problem with analytical spectra, yielding a simple linear relation between the number of converged eigenvalues and the number of grid points. We then apply the analysis to Taylor-Culick flow, yielding a similar relation for the converged eigenvalue points. We find that the structural error analysis provides reliable criteria for the grid computation in flow stability analysis of a real solid rocket motor. In studies involving numerical spectra, the proposed structural error provides an alternative tool for error analysis of problems such as Taylor-Culick flow, where the computed individual eigenvalues do not necessarily converge to fixed values with increasing grid refinement.