Development of a prefactored high-order compact scheme for low-speed aeroacoustics

A new class of cost-optimized prefactored high-order compact schemes is developed for shockfree error-bounded aeroacoustic applications. The cost-optimization theory of Pirozzoli (2007), based on the minimization of the computational cost for a given level of error, is applied to a class of prefactored compact sixth-order schemes. They are extended to obtain a new class of time-explicit cost-optimized schemes. Appropriate high-order prefactored boundary closures are coupled with the new interior schemes. Their effect on the stability and accuracy of the interior schemes and their wave propagation characteristics in Fourier space are investigated. More conventional non-reflecting boundary conditions are shown to display an impedance mis-match, reducing the order of accuracy of the overall scheme. An 11-point stencil with double precision accuracy is used as the prefactored interior boundary stencil. It shows a better performance in spectral sense compared to the equivalent ones available in literature. An eigenvalue analysis is performed, to verify the stability of the prefactored cost-optimized schemes coupled with the boundary closures. Characteristics based boundary conditions and absorbing layers are evaluated. A parallelization strategy, based on a finite-sized overlapping interface, is presented and weak scalability tests results are shown. The theoretical roll-off error of the new schemes agree well with the computed norm error roll-off between the analytical prediction and the numerical experiments, for a monochromatic sinusoidal test-case. There is a good agreement between the predicted percentage cost-saving of the one-dimensional cost function and the savings in computational time from the numerical tests. A 22% computational cost-saving at the design level of error is achieved. Sample applications to broadband and two-dimensional space benchmark problems demonstrate the low error-bounded and high-order accuracy characteristics of the baseline scheme for aeroacoustic applications.