Bandwidth-Optimized Summation-by-Parts Operators for High-Resolution Turbulent Flow Simulations

Three new, bandwidth-optimized, 4^th-order-accurate finite-difference schemes are introduced with boundary closures that satisfy the summation-by-parts convention. These schemes include a conventional-form interior scheme with diagonal norm and two Padé-type schemes, one with a pentadiagonal norm and one with a tridiagonal norm. It is proven that tridiagonal Padé schemes are limited to 1st-order boundary closures for the commonly used structure of the implicit and explicit sides, whereas 3^rd-order closure was achievable with a pentadiagonal norm. Modified wavenumber analyses are presented to show the spectral resolution of the various schemes, and various test cases are considered to evaluate their efficacy. After this evaluation, the optimized conventional scheme with diagonal boundary closure appeared to have the best combination of resolution, stability, and computational efficiency.