Flux difference splitting for the Euler equations in one spatial co‐ordinate with area variation

Abstract

AbstractAn approximate (linearized) Riemann solver is presented for the solution of the Euler equations of gas dynamics in one spatial co‐ordinate. This includes cylindrically and spherically symmetric geometries and also applies to narrow ducts with area variation. The method is Roe's flux difference splitting with a technique for dealing with source terms. The results of two problems, a spherically divergent infinite shock and a converging cylindrical shock, are presented. The numerical results compare favourably with those of Noh's recent survey and also with those of Ben‐Artzi and Falcovitz using a more complicated Riemann solver.