All methods of solving the Euler equations face the problem of errors in entropy. These errors are especially important at the leading edge of blade rows where any numerical errors will cause entropy to be produced and to convect downstream to influence the downstream flow, especially that on the blade surfaces.
A new numerical method is described which overcomes this problem by solving a conservation equation for entropy. This equation effectively replaces the usual momentum equation along streamlines. Sources of entropy are introduced to allow for shock loss with the magnitude of the source being determined from the Rankine-Hugoniot relations. A semi-implicit scheme is used to solve the continuity equation whilst the entropy and flow direction are updated by conventional explicit methods.
The flow through a selection of test cascades has been calculated with this new method and its predictions compared with exact solutions as well as with experimental data and with a conventional Euler solver. The results show that the new method is more accurate than the conventional one, it converges in fewer iterations but requires slightly longer computer times.