A new strategy towards stable and accurate boundary closures for high-order finite difference schemes

Wu, Long and Kim, Jae-Wook (2024) A new strategy towards stable and accurate boundary closures for high-order finite difference schemes. In 30th AIAA/CEAS Aeroacoustics Conference (2024). (doi:10.2514/6.2024-3361).

Record type: Conference or Workshop Item (Paper)

Abstract

This paper presents a generalised strategy to develop linearly stable and accurate boundary closure schemes for large-stencil, high-order, finite difference systems in computational aero acoustics. The optimisation problem is formulated to maximise the global accuracy of the differencing system under a linear stability constraint evaluated by eigenvalue analysis. The strategy for constructing boundary schemes is based on an interpolation-differentiation procedure. Three sets of optimised boundary closure schemes have been presented for three widely used central schemes in computational aero acoustics. The present boundary schemes, when used together with the corresponding central scheme, are guaranteed to be linearly stable. Moreover, they are more accurate compared with the previous boundary schemes optimised for resolution.

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