Embedded WENO : a design method to improve existing WENO schemes

Embedded WENO methods utilize all adjacent smooth substencils to construct a desirable interpolation. Conventional WENO schemes underuse this possibility close to large gradients or discontinuities. Embedded methods based on the WENO schemes of Jiang and Shu [1] and on the WENO-Z scheme of Borges et al. [2] are explicitly constructed. Several possible choices are presented that result in either better spectral properties or a higher order of convergence. The embedded methods are demonstrated to be improvements over their standard counterparts by several numerical examples. All the embedded methods presented have virtually no added computational effort compared to their standard counterparts. Keywords: Essentially non-oscillatory, WENO, high-resolution scheme, hyperbolic conservation laws, nonlinear interpolation, spectral analysis