Abstract
A finite volume method for the simulation of compressible aerodynamic flows is described. Stabilisation and shock capturing is achieved by the use of an HLLC consistent numerical flux function, with acoustic wave improvement. The method is implemented on an unstructured hybrid mesh in three dimensions. A solution of higher order accuracy is obtained by reconstruction, using an iteratively corrected least squares process, and by a new limiting procedure. The numerical performance of the complete approach is demonstrated by considering its application to the simulation of steady turbulent transonic flow over an ONERA M6 wing and to a steady inviscid supersonic flow over a modern military aircraft configuration.