Abstract
In this paper, we design a new type of high order weighted compact scheme based on ZJS method (Zhang et al., 2008) [35] and ZQ method (Zhu and Qiu, 2016) [16]. These nonlinear weighted compact schemes are designed based on the cell-centered compact scheme of Lele (Lele, 1992) [22]. Instead of using WENO interpolation with equal-sized sub-stencil in ZJS formulae in Zhang et al. (2008) [35] for the fluxes on the cell centers, a new type of WENO interpolation with unequal sized sub-stencil is proposed following the similar idea of WENO reconstruction by Zhu and Qiu (2016) [16]. Through systematic numerical tests and comparisons with the weighted compact schemes and traditional WENO scheme, we observe that the new type weighted compact scheme has better resolution, smaller dissipation, while the ability to capture strong shock waves is maintained.
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