We were pleasantly surprised by the ready acceptance of the first edition of our book by the CFD community and by the amount of positive feedback received over a period of 10 years. To us this has provided justification of our original plan， which was to provide an accessible introduction to this fast-growing topic to support teaching at senior undergraduate level， post- graduate research and new industrial users of commercial CFD codes. Our second edition seeks to enhance and update. The structure and didactic approach of the first edition have been retained without change， but aug- mented by a selection of the most important developments in CFD.