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

Jianxian Qiu

Rémi Abgrall

邱建贤

Journal of Computational Physics

Xiamen University Institutional Repository

Journal of Computational Physics 230 (2011) 4101–4102Contents lists available at ScienceDirectJournal of Computational Physicsjournal homepage: www.elsevier .com/locate / jcpEditorialPreface 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 forsteady and unsteady problems. Within Europe and the US, several conferences deal with these issues, some of them havebeen 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 verycomplex problems.When dealing with complex geometries, such as part or full aircraft, several difficult issues have to be addressed:1. Accuracy and robustness: the same method has to be able to deal with smooth and non smooth flows. Since the geometryis in general complex, unstructured meshes are most often used, so that one has to understand in detail how to use nonlinear filtering methods, such as limiters, to remove spurious oscillations without spoiling the accuracy in smoothregimes.2. Mesh generation: one of the key issue is to generate meshes where the geometry is accurately represented, and thenumerical method able to handle this easily,3. The volume of computation: the number of degrees of freedom increase very quickly, so that it becomes uneasy to visu-alize them. More over, it is not clear whether or not current visualization tool are adapted to data structure generated byhigh order schemes, probably not.4. In order to lower the number of degree of freedom and to make computations simply doable, tools are mesh adaptation,in particular goal oriented mesh adaptation.This interest has reached the industry community rising new problems to the academic community. For example, thespecific target research project ‘‘Adaptive higher-order variational methods for aerospace applications’’ (ADIGMA) was ini-tiated within the 3rd Call of the 6th European Research Framework Programme (2006–2009) [10] has gathered academicteams from Europe and one from China,1 Research institutes2 and industrial partners3 The papers contained in this specialissue are mostly coming from ADIGMA partners, but not only since we have tried to open the community and the range ofmethods.More specially, the following items are covered:1. Approximation. The approximation of the Euler and Navier–Stokes equations is covered by [13,1,5] using residual distri-bution schemes, and [7,4,12,16] with Discontinuous Galerkin methods. Other kind of high order approximation are alsocovered such as high order finite differences [6], iso-geometric analysis [2], and artificial viscosity methods [8] or lowdissipative methods [14].2. Efficiency in the solvers in [15,3].3. Some adaptation strategies [9], other can be found (with second order methods) in [11].The development of efficient and reliable very high order scheme is still an ongoing work, according to the abundant lit-erature and workshops, see for example the 1st International Workshop on High-Order CFD Methods http://www.public.ias-tate.edu/zjw/hiocfd.html.0021-9991/$ - see front matter  2011 Elsevier Inc. All rights reserved.doi:10.1016/j.jcp.2011.03.0041 The complete list is the University degli Studi di Bergamo (Italy), Ecole Nationale Supérieure des Arts et Métiers (Paris, France), the University ofNottingham (UK), Charles University (Prague, Czech Republic), the University of Wales (Swansee, UK), The University of Stuttgard (Germany), UppsalaUniversity (Sweden), the University of Twente (The Nerderlands), Warsaw University of Technology (Poland), Najing University (PR China).2 ARA (UK), DLR (Germany), ONERA (France), INRIA (France), VKI (Belgium).3 Alenia Aeronautica (Italy), Airbus (France and Germany), Dassault Aviation (France), EADS-MAS (Germany) and CENAERO (Belgium).4102 Editorial / Journal of Computational Physics 230 (2011) 4101–4102AcknowledgementsR. Abgrall has been funded by the ERC Advanced Grant ‘‘ADDECCO’ # 226316, J. Qiu has been funded by NSFC 10931004.R. Abgrall and J. Qiu would like to thank P. Degond for handling one of the papers in this special issue.References[1] R. Abgrall, A. Larat, M. Ricchiuto, Construction of very high order residual distribution schemes for steady inviscid flow problems on hybridunstructured meshes, J. Comput. Phys. 230 (11) (2011) 4103–4136.[2] I. Akkerman, Y. Bazilevs, C. Kees, M. Farthing, Isogeometric analysis of free-surface flow, J. Comput. Phys. 230 (11) (2011) 4137–4152.[3] F. Bassi, A. Ghidoni, S. Rebay, Optimal runge-kutta smootehrs for the p-multigrid discontinuous galerkin solution of the 1d Euler equations, J. Comput.Phys. 230 (11) (2011) 4153–4175.[4] V. Dolejsi, M. Holik, J. Hozman, Efficient solution strategy for the semi-implicit discontinuous galerkin discretization of the Navier–stokes equations, J.Comput. Phys. 230 (11) (2011) 4176–4200.[5] Xi Du, C. Corre, A. Lerat, A third-order finite-volume residual-based scheme for the 2d Euler equations on unstructured grids, J. Comput. Phys. 230 (11)(2011) 4201–4215.[6] S. Eriksson, Q. Abbas, J. Nordstrom, A stable and conservative method for locally adapting the design order of finite difference schemes, J. Comput. Phys.230 (11) (2011) 4216–4231.[7] G. Gassner, M. Dumbser, F. Hindenlang, C.-D. Munz, Explicit one–step time discretizations for discontinuous galerkin and finite volume schemes basedon local predictors, J. Comput. Phys. 230 (11) (2011) 4232–4247.[8] J.L. Guermond, B. Popov, R. Pasquetti, Entropy viscosity method for nonlinear conservation laws, J. Comput. Phys. 230 (11) (2011) 4248–4267.[9] R. Hartmann, J. Held, T. Leicht, Adjoint-based error estimation and adaptive mesh refinement for the rans and k–x turbulence model equations, J.Comput. Phys. 230 (11) (2011) 4268–4284.[10] N. Kroll, H. Bieler, H. Deconinck, V. Couaillier, H. van der Harmen, K. Sorensen, ADIGMA: a European initiative on the development of adaptive higher-order variational methods for aerospace applications, Notes on Numerical Fluid Mechanics and Multidisciplinary Design, vol. 113, Springer-Verlag,2010.[11] A. Loseille, A. Dervieux, F. Alauzet, Fully anisotropic goal-oriented mesh adaptation for 3d steady euler equations, J. Comput. Phys. 229 (8) (2010)2866–2897.[12] D.J. Mavriplis, C. Nastase, On the geometric conservation law for high-order discontinuous galerkin discretizations on dynamically deforming meshes,J. Comput. Phys. 230 (11) (2011) 4285–4300.[13] N. Villedieu, T. Quintino, M. Ricchiuto, H. Deconinck, Third order residual distribution schemes for the Navier–stokes equations, J. Comput. Phys. 230(11) (2011) 4301–4315.[14] Wei Wang, H.C. Yee, B. Sjogreen, T. Magin, C.-W. Shu, Construction of low dissipative high-order well-balanced filter schemes for non-equilibriumflows, J. Comput. Phys. 230 (11) (2011) 4316–4335.[15] Yong-Tao Zhang, Krylov implicit integration factor methods for spatial discretization on high dimensional unstructured meshes: application todiscontinuous galerkin methods, J. Comput. Phys. 230 (11) (2011) 4336–4352.[16] Jun Zhu, Jianxian Qiu, Local dg methods using weno type limiters for convection-diffusion problems, J. Comput. Phys. 230 (11) (2011) 4353–4375.Rémi AbgrallTeam Bacchus,INRIA and Institut de Mathématiques de Bordeaux,Bordeaux Sud Ouest and Université de Bordeaux,33 405 Talence, FranceTel.: +33 5 40 00 60 68; fax: +33 5 40 00 26 26E-mail address: remi.abgrall@inria.frJianxian QiuSchool of Mathematical Science,Xiamen University,Xiamen, Fujian 361005,ChinaDepartment of Mathematics,Nanjing University,Nanjing,Jiangsu 210093,ChinaAvailable online 4 March 2011

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

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

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