Preliminary results on the extension of eno schemes to two-dimensional problems

Abstract

In this paper we present preliminary results on the extension of high-order accurate essentially non-oscillatory (ENO) schemes to the solution of hyperbolic systems of conservation laws in 2D. The design involves an essentially non-oscillatory piecewise polynomial reconstruction of the solution from its cell averages, solution in the small of the resulting piecewise polynomial initial value problem, and averaging of this solution over each cell. Unlike standard finite difference methods this procedure uses an adaptive stencil of grid points and consequently the resulting schemes are highly nonlinear.