A cure for the sonic point glitch

Among the various numerical schemes developed since the '80s for the comput ation of the compressible Euler equations, the vast majority produce in cer tain cases spurious pressure glitches at sonic points. This flaw is particu larly visible in the computation of transonic expansions and leads to unphy sical "expansion shocks" when the flow undergoes rapid change of direction. The analysis of this Raw is presented, based on a series of numerical exper iments. For Flux-Vector Splitting methods, it is suggested that it is not t he order of differentiability of the numerical flux which is crucial but th e way the pressure at an interface is calculated. A new way of evaluating t he pressure at the interface is proposed, based upon kinetic theory, and is applied to most current available algorithms including Flux-Vector Splitti ng and Flux-Difference Splitting methods as well as recent hybrid schemes ( AUSM, HUS).