Flux difference splitting for the Euler equations in generalised coordinates using a local parameterisation of the equation of state

An efficient algorithm based on flux difference splitting is presented for the solution of the three-dimensional Euler equations of gas dynamics in a generalised coordinate system with a general equation of state. The scheme is based on solving linearised Riemann problems approximately and in more than one dimension incorporates operator splitting. The algorithm uses a local parameterisation of the equation of state and as a consequence requires only one function evaluation in each computational cell. The scheme has good shock capturing properties and the advantage of using body-fitted meshes. Numerical results are shown for Mach 8 flow of equilibrium air past a circular cylinder.This work forms part of the research programme for the Institute of Computational Fluid Dynamics at the Universities of Oxford and Reading and was funded by AWRE, Aldermaston under Contract No. NSN/13B/2A88719.