WENO Reconstructions of Unconditionally Optimal High Order

A modified weighted essentially nonoscillatory (WENO) reconstruction technique preventing accuracy loss near critical points (regardless of their order) of the underlying data is presented. This approach only uses local data from the reconstruction stencil and does not rely on any sort of scaling parameters. The key novel ingredient is a weight design based on a new smoothness indicator, which defines the first WENO reconstruction procedure that...