Typical Riemann-solver based CFD algorithms using flux formulations like the Roe-flux-difference-splitting (Roe-FDS) employ preconditioning techniques to eliminate the numerical stiffness in low-Mach number regimes and improve accuracy for all speed flows. For low-Mach flows it has been shown in [3] that the numerical flux dissipation required for high-Strouhal number, unsteady simulations must be different from the one used at low-Strouhal numbers, or for steady flow problems. Proper unsteady, low-Mach preconditioning should have the effect of clustering together the convective and acoustic eigenvalues, while at the same time introducing just the appropriate amount of numerical dissipation over all ranges of Strouhal number. Following an idea introduced by Hosangadi et al. for the AUSM+up type schemes, we propose an enhancement to the preconditioned Roe-flux to reduce its numerical dissipation and improve convergence per time-step for the range of Mach and Strouhal numbers typical of CAA applications. Our modifications for the preconditioned Roe-FDS flux provide the same benefits seen for the AUSM+up type flux, and involve no user specified parameters or tuning. The performance achieved by our Roe-flux formula enhancement is demonstrated through a few numerical experiments.
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