Verification of a fluid-dynamics solver using correlations with linear stability results

A novel method is described for verification of fluid-dynamics solvers based on correlations with solutions from linear stability analysis. A difficulty with the linear stability analysis solutions for spatially developing flows is that flow fields typically exhibit exponentially growing features compromising the performance of classical error metrics. This motivates the construction of a projection-based metric that only assumes the shape of the solution and not the growth rate of the perturbations, thus also allowing the latter to be determined. The proposed correlation metric complements classical error metrics, such as p-norms, and can also be used for time-dependent problems with realistic boundary conditions. We demonstrate how the present method can be applied in the verification of an Euler solver for the instability behavior of laminar compressible free and confined shear layers.