On consistent boundary closures for compact finite-difference WENO schemes

The accuracy of compact finite-difference schemes can be degraded by inconsistent domain or box boundary treatments. A consistent higher-order boundary closure is especially important for block-structured Cartesian AMR solvers, where the computational domain is generally decomposed into a large number of boxes containing a relatively small number of grid points. At each box boundary, a consistent higher-order boundary closure needs to be applied to avoid a reduction of the formal order-of-accuracy of the numerical scheme. This paper presents such a boundary closure for the fifth-order accurate compact finite-difference WENO scheme by Ghosh and Baeder [1]. The accuracy of the new boundary closure is validated by employing the method of manufactured solutions. A comparison of the new compact boundary closure with the original explicit boundary closure demonstrates the improved accuracy for the new compact boundary closure, while the behavior of the scheme across discontinuities appears unaffected. The linear stability analysis results indicate that a linearly stable compact WENO boundary closure is achieved.