Efficient shock capturing for isentropic flows using arithmetic averaging

Glaister, P. (1994) Efficient shock capturing for isentropic flows using arithmetic averaging. International Journal of Numerical Methods for Heat and Fluid Flow, 4 (5). pp. 453-463. ISSN 0961-5539 doi: 10.1108/EUM0000000004049

Abstract/Summary

A shock capturing scheme is presented for the equations of isentropic flow based on upwind differencing applied to a locally linearized set of Riemann problems. This includes the two-dimensional shallow water equations using the familiar gas dynamics analogy. An average of the flow variables across the interface between cells is required, and this average is chosen to be the arithmetic mean for computational efficiency, leading to arithmetic averaging. This is in contrast to usual ‘square root’ averages found in this type of Riemann solver where the computational expense can be prohibitive. The scheme is applied to a two-dimensional dam-break problem and the approximate solution compares well with those given by other authors.