Performance of WENO Scheme in Generalized Curvilinear Coordinate Systems

The weighted-essentially non-oscillatory (WENO) schemes have been used to calculate the shock-embedded compressible fluid flow ([9]). The potential high-fidelity qualities of this approach make it attractive for jet noise simulation. However, in its present form, the WENO procedure has many drawbacks that prevent direct applications to jet noise simulations. In this paper, various WENO procedures are evaluated in generalized curvilinear coordinate systems. In addition, freestream preservation and boundary treatment are discussed. It has been verified in this paper that the original WENO procedure drafted by Jiang and Shu ([9]) is too dissipative for shock/entropy wave interactions. It has also been found that the ghost-point boundary treatment suggested in [9] does not perform well for shock-boundary interaction problems and more general problems with solid walls. Furthermore, it is demonstrated that the modifications suggested by Martin et al. ([11], [12]) are susceptible to numerical oscillations in non-homogeneous compressible flows. A modified WENO scheme that is more robust and less dissipative is proposed and tested in this paper.