ENO Schemes with Subcell Resolution*

Abstract

In this paper, we introduce the notion of subcell resolution, which is based on the observation that unlike point values, cell-averages of a discontinuous piecewise-smooth function contain information about the exact location of the discontinuity within the cell. Using this observation we design an essentially non-oscillatory (ENO) reconstruction technique which is exact for cell averages of discontinuous piecewise-polynomial functions of the appropriate degree. Later on we incorporate this new reconstruction technique into Godunov-type schemes in order to produce a modification of the ENO schemes which prevents the smearing of contact discontinuities.

Research was supported under NSF Grant DMS85-03294, DARPA Grant in the ACMP Program, ONR Grant N00014-86-K-0691, NASA Ames Interchange NCA2-185, and NASA Langley Grant NAG1-270. Also research was partially supported under the National Aeronautics and Space Administration under NASA Contract NAS1-18107 while the author was in residence at the Institute for Computer Applications in Science and Engineering (ICASE), NASA Langley Research Center, Hampton, VA 23665-5225.