VERY HIGH-ORDER SPATIALLY IMPLICIT SCHEMES FOR COMPUTATIONAL ACOUSTICS ON CURVILINEAR MESHES

TLDR

A high‑order compact‑differencing and filtering algorithm, combined with a classical fourth‑order Runge–Kutta scheme, is developed to simulate aeroacoustic phenomena on curvilinear geometries, addressing several pertinent issues. The scheme employs a discriminating higher‑order filter to mitigate mesh‑stretching‑induced high‑frequency spurious modes, uses special metric relations for 3‑D curvilinear meshes, and integrates the algorithm with the Runge–Kutta time stepping. Filtering enables robust outflow radiation treatment, higher‑order one‑sided filters improve accuracy and stability over explicit variants, and the combined approach successfully handles interface treatments in multi‑domain strategies, as demonstrated by benchmark computations.

Abstract

A high-order compact-differencing and filtering algorithm, coupled with the classical fourth-order Runge–Kutta scheme, is developed and implemented to simulate aeroacoustic phenomena on curvilinear geometries. Several issues pertinent to the use of such schemes are addressed. The impact of mesh stretching in the generation of high-frequency spurious modes is examined and the need for a discriminating higher-order filter procedure is established and resolved. The incorporation of these filtering techniques also permits a robust treatment of outflow radiation condition by taking advantage of energy transfer to high-frequencies caused by rapid mesh stretching. For conditions on the scatterer, higher-order one-sided filter treatments are shown to be superior in terms of accuracy and stability compared to standard explicit variations. Computations demonstrate that these algorithmic components are also crucial to the success of interface treatments created in multi-domain and domain-decomposition strategies. For three-dimensional computations, special metric relations are employed to assure the fidelity of the scheme in highly curvilinear meshes. A variety of problems, including several benchmark computations, demonstrate the success of the overall computational strategy.