A new method towards high-order weno schemes on structured and unstructured grids

Abstract A new method is presented to develop high-order weighted essentially non-oscillatory (WENO) finite-volume schemes on structured and unstructured grids. The one-dimensional reconstruction used in the WENO-ZQ scheme is extended by introducing the concept of phantom points, which are constructed with the least-squares approximation to form a series of high-order WENO schemes. Numerical validations are performed on both regular structured grids and irregular unstructured grids. Analyses of the spectral property and numerical accuracy of the new schemes indicate attractive merits, including less dissipation and dispersion errors and low computational costs, which can be easily implemented into existing structured and unstructured grid CFD solvers.

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