  ENO (Essentially Non-Oscillatory) and WENO (Weighted Essentially
Non-Oscillatory) schemes are widely used high-order schemes for solving partial
differential equations (PDEs), especially hyperbolic conservation laws with
piecewise smooth solutions. For structured meshes, these techniques can achieve
high order accuracy for smooth functions while being non-oscillatory near
discontinuities. For unstructured meshes, which are needed for complex
geometries, similar schemes are required but they are much more challenging. We
propose a new family of non-oscillatory schemes, called WLS-ENO, in the context
of solving hyperbolic conservation laws using finite-volume methods over
unstructured meshes. WLS-ENO is derived based on Taylor series expansion and
solved using a weighted least squares formulation. Unlike other non-oscillatory
schemes, the WLS-ENO does not require constructing sub-stencils, and hence it
provides more flexible framework and is less sensitive to mesh quality. We
present rigorous analysis of the accuracy and stability of WLS-ENO, and present
numerical results in 1-D, 2-D, and 3-D for a number of benchmark problems, and
also report some comparisons against WENO.
