A Hybrid Optimized Difference Scheme

The optimized difference scheme, which is applied for computational aeroacoustics(CAA) problems and direct numerical simulations(DNS) of compressible turbulent flows, is generally designed for better resolution on short waves. However, the accuracy order of the scheme is usually decreased in the optimization procedure. In this paper, a hybridization of the optimized scheme and the highest order scheme was proposed to improve the convergence accuracy and the spectral resolution. This is a weighted convex combination of the two schemes. The weight is determined by the value in the stencil and thus the final scheme is nonlinear. The phase error is reduced substantially for problems of monochromatic waves. But the computational cost is increased because of the weighted hybridization. Numerical tests validate the good property of the proposed scheme.