  Finite difference method was extended to unstructured meshes to solve Euler
equations. The spatial discretization is made of two steps. First, numerical
fluxes are computed at the middle point of each edge with high order accuracy.
In this step, a one-dimensional curvilinear stencil is assembled for each edge
to perform one-dimensional fast non-uniform WENO interpolation derived in this
paper, which is much easier and faster than multi-dimensional interpolation.
The second step is to compute the divergence of fluxes at each vertex from the
fluxes at nearby edges and vertices by least square approximation of
multi-dimensional polynomials. The order of the WENO interpolation in the first
step and the degree of the polynomial in the second step determined the order
of accuracy of the spatial scheme. After that, explicit RungeKutta time
discrete scheme is used to update conservative variables. Several canonical
numerical cases were solved to test the accuracy, performance and the
capability of shock capturing of the developed method.
