Book Description

The verification of numerical schemes for solving the equations of inviscid and viscous compressible unsteady flow equations is limited to a small number of analytical solutions of the equations governing the one-dimensional unsteady flow including moving discontinuities. Among them the most important were given first by B Riemann (1859.1860) and later by W.J.M RanKine (1870), P.H. Hugoniot (1887), Lord Rayleigh (1910) and GI. Taylor (1910). The scope of the present chapter is to overview the analytical solutions, serving as test case for the accuracy of the numerical schcmes. It is worth noting that the analytical solutions are of importance for Euler and Navier-Stokes equations for laminar flow and does not give any indication for the behaviour of the numerical schemes in the prediction of turbulent flows. For each analytical solution a corresponding FORTRAN program is attached.