A Piecewise-parabolic dual-mesh method for he euler equations

摘要

A piecewise-parabolic dual-mesh method for the one-dimensional Euler equations is presented. The method carries the cell averages as well as the interface values of the conserved variables and, for this reason, has very small dissipation and dispersion errors. Oscillations in the solutions are avoided by devising monotonicity constraints that preserve accuracy near extrema. A steepening technique that can capture contact discontinuities in two cells is introduced. A dual-(staggered) mesh system, which facilitates the updating of both variables (avcerages and point values), is employed. The resulting method is a centered scheme and can be considered a third-order accurate extension of the Lax-Friedrichs method.