Novel High‐Order Alternative Finite Difference Central WENO Schemes for Hyperbolic Conservation Laws.

The fifth‐order alternative finite difference weighted essentially non‐oscillatory (A‐WENO5) scheme is dominated by the truncation error of interpolation, resulting in a loss of one order of accuracy, despite the sixth‐order Taylor expansion of flux terms. In this study, we introduce the central WENO (CWENO) interpolation process in the A‐WENO5 framework to recover the optimal order and design fifth‐ and sixth‐order alternative CWENO schemes for solving the hyperbolic conservation laws. The key point is to enhance the interpolation procedure of the central stencil to realize the optimal sixth‐order accuracy. The linear weights are determined through approximate dispersion relation analysis, which also indicates a significant reduction in numerical dissipation compared with the A‐WENO5 scheme. Combining affine‐invariant WENO operators and Taylor analysis, the new local and global smoothness indicators are designed. The proposed schemes present many benefits, including lower dissipation, optimal order in truncation error, flexibility in choosing linear weights, and fewer CPU timings besides capturing the discontinuous solutions without numerical oscillations in contrast to the classical A‐WENO5 scheme. [ABSTRACT FROM AUTHOR]