Multi-Dimensional ENO Schemes for General Geometries

Abstract : In this paper we present a class of ENO schemes for the numerical solution of multidimensional hyperbolic systems of conservation laws in structured and unstructured grids. This is a class of shock-capturing schemes which are designed to compute cell-averages to high-order accuracy. The ENO scheme is composed of a piecewise-polynomial reconstruction of the solution from its given cell averages, approximate evolution of the resulting initial value problem , and averaging of this approximate solution over each cell. The reconstruction algorithm is based on an adaptive selection of stencil for each cell so as to avoid spurious oscillations near discontinuities while achieving high order of accuracy away from them.