172 1996 Bjorn Sjogreen bjorns@tdb.uu.se A New ENO Scheme Abstract Present ENO schemes are either based on cell averages with ENO interpolation on the primitive function of the approximation, or finite difference schemes with ENO interpolation on the flux functions. We here present a finite difference ENO scheme using ENO interpolation on the approximation. The new scheme is the generalization of the MUSCL scheme, seen in a finite difference context. The advantages of the new method are a) great flexibility in the choice of first order building block scheme b) conceptual simplicity since ENO interpolation is done directly on the approximation c) easy to generalize to three space dimensions, since it is a finite difference method d) correct treatment of curvilinear grids, geometrical source terms can be avoided.