WEIGHTED ESSENTIALLY NONOSCILLATORY SCHEMES

In this paper we introduce a new version of ENO (essentially non-oscillatory) shock-capturing schemes which we call weighted ENO. The main new idea is that, instead of choosing the ''smoothest'' stencil to pick one interpolating polynomial for the ENO reconstruction, we use a convex combination of all candidates to achieve the essentially non-oscillatory property, while additionally obtaining one order of improvement in accuracy. The resulting weighted ENO schemes are based on cell averages and a TVD Runge-Kutta time discretization. Preliminary encouraging numerical experiments are given. (C) 1994 Academic Press, Inc.