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In this work, effect of using an adaptive central-upwind (ACU) interpolation on weighted compact non-linear scheme (WCNS) is investigated. Based on the smoothness of solution, this type of interpolation adapts between central and upwind stencils by a weighting relation and combination of smoothness indicators of the optimal high-order stencil and its sub-stencils. The coefficients of sixth to tenth order ACU-WCNS are calculated and truncation error analysis and wavenumber analysis are performed to evaluate basic numerical characteristics of this new schemes. Order of accuracy is validated by one dimensional advection equation and by applying ACU-WCNS on several benchmark problems, its shock-capturing abilities, its behavior in presence of severe discontinuity and its numerical resolution in shock-entropy interaction are investigated.

high-order numerical method; Weighted compact nonlinear scheme; shock-capturing; compressible flow