Preface to the special issue 'High order methods for CFD problems'

Since a few years, there has been a renew in interest in (very) high order schemes for compressible fluid dynamics for steady and unsteady problems. Within Europe and the US, several conferences deal with these issues, some of them have been launched only recently. Several special issues of recent or future AIAA conferences are specially devoted to that topic. The goal of these researches is to design cheaper and more efficient numerical methods able to handle very large and very complex problems

A stable and conservative method for locally adapting the design order of finite difference schemes

A procedure to locally change the order of accuracy of finite difference schemes is developed. The development is based on existing Summation-By-Parts operators and a weak interface treatment. The resulting scheme is proven to be accurate and stable.   Numerical experiments verify the theoretical accuracy for smooth solutions. In addition, shock calculations are performed, using a scheme where the developed switching procedure is combined with the MUSCL technique.Original Publication:Sofia Eriksson, Qaisar Abbas and Jan Nordström, A stable and conservative method for locally adapting the design order of finite difference schemes, 2011, Journal of Computational Physics, (230), 11, 4216-4231.http://dx.doi.org/10.1016/j.jcp.2010.11.020Copyright: Elsevier Science B.V., Amsterdamhttp://www.elsevier.com