182
Views
9
CrossRef citations to date
0
Altmetric
Articles

Semi-meshless stencil selection for anisotropic point distributions

, , &
Pages 463-487 | Received 12 Sep 2012, Accepted 22 Oct 2012, Published online: 13 Dec 2012

References

  • Aftosmis , M.J. Solution adaptive Cartesian grid methods for aerodynamic flows with complex geometries . VKI Lecture Series, 1997-02, 28th computational fluid dynamics . March 3–7 .
  • Aftosmis , M.J. , Berger , M.J. and Melton , J.E. Robust and efficient Cartesian mesh generation for component-based geometry . AIAA Journal, 31, 1–17 .
  • Anandhanarayanan , K. 2010 . Development of three-dimensional grid-free solver and its applications to multi-body aerospace vehicles . Defence Science Journal , 60 ( 6 ) : 653 – 662 .
  • Badcock , K.J. , Richards , B.E. and Woodgate , M.A. 2000 . Elements of computational fluid dynamics on block structured grids using implicit solver . Progress in Aerospace Sciences , 36 : 351 – 392 .
  • Barth , T.J. and Jespersen , D.C. The design and application of upwind schemes on unstructured meshes. In: 27th AIAA Aerospace Sciences Meeting, Reno, NV . AIAA paper 89-0366 .
  • Batina , J.T. 1992 . “ A gridless Euler/Navier-Stokes solution algorithm for complex two dimensional applications ” . In NASA Technical Memorandum 107631 , Hampton , VI : National Aeronautics and Space Administration, NASA Langley Research Center .
  • Belytschko , T. 1996 . Meshless methods: an overview and recent development . Computer Methods in Applied Mechanics and Engineering , 139 ( 1–4 ) : 3 – 47 .
  • Bonet , J. and Peraire , J. 1991 . An alternating digital tree (ADT) algorithm for 3D geometric searching and intersection problems . International Journal for Numerical Methods in Engineering , 31 ( 1 ) : 1 – 17 .
  • Chiu , E. and Jameson , A. An edge-averaged semi-meshless framework for numerical solution of conservation laws . AIAA Paper 2010-1269, 48th AIAA Aerospace Sciences Meeting .
  • Fries , T. and Matthies , H. 2004 . “ Classification and overview of meshfree methods. Informatikbericht-Nr. 2003-03 ” . In Department of Mathematics and Computer Science , Technical University of Braunschweig .
  • Idelsohn , S.R. and Oñate , E. 2006 . To mesh or not to mesh. That is the question …  . Computer Methods in Applied Mechanics and Engineering , 195 ( 37–40 ) : 4681 – 4696 .
  • Jameson , A. Time dependent calculations using multigrid, with applications to unsteady flows past airfoils and wings . AIAA Paper 91-1596, AIAA 10th Computational Fluid Dynamics Conference .
  • Jawahar , P. and Kamath , H. 2000 . A high-resolution procedure for Euler and Navier–Stokes computations on unstructured grids . Journal of Computational Physics , 164 : 165 – 203 .
  • Kamruzzaman , M. 2007 . A new meshless collocation method for partial differential equations . Journal of Communications in Numerical Methods in Engineering , 24 ( 4 ) : 1617 – 1639 .
  • Katz , A. , Jameson , A. and Wissink , A. A multi-solver scheme for viscous flows using adaptive Cartesian grids and meshless grid communication . AIAA Paper 2009-768, 47th AIAA Aerospace Sciences Meeting including The New Horizons Forum and Aerospace Exposition .
  • Kennett , D.J. 2012 . An implicit meshless method for application in computational fluid dynamics . International Journal of Numerical Methods in Fluids , doi: 10.1002/fld.3698
  • Liao , W. , Cai , J. and Tsai , H.M. 2007 . A multigrid overset grid flow solver with implicit hole cutting method . Computer Methods in Applied Mechanics and Engineering , 196 : 1701 – 1715 .
  • Liszka , T.J. , Duarte , C.A.M. and Tworzydlo , W.W. 1996 . hp-Meshless cloud method . Computer Methods in Applied Mechanics and Engineering , 139 : 263 – 288 .
  • Löhner , R. 2002 . A finite point method for compressible flow . International Journal for Numerical Methods in Engineering , 53 ( 8 ) : 1765 – 1779 .
  • Mavripilis , D.J. Unstructured mesh discretisations and solvers for computational aerodynamics . AIAA Paper 2007-3955, 18th AIAA Computational Fluid Dynamics Conference .
  • Munikrishna , N. and Balakrishnan , N. 2011 . Turbulent flow computations on a hybrid Cartesian point distribution using meshless solver LSFD-U . Computers and Fluids , 40 ( 1 ) : 118 – 138 .
  • Ortega , E. , Oñate , E. and Idelsohn , S. 2007 . An improved finite point method for tridimensional potential flows . Computational Mechanics , 40 ( 6 ) : 949 – 963 .
  • Roe , P.L. 1981 . Approximate Riemann solvers, parameter vectors and difference schemes . Journal of Computational Physics , 43 : 357 – 372 .
  • Samet , H. 1984 . The quadtree and related hierarchical data structures . Computing Surveys , 16 ( 2 ) : 187 – 260 .
  • Seibold , B. 2008 . Minimal positive stencils in meshfree finite difference methods for the Poission equation . Computer Methods in Applied Mechanics and Engineering , 198 ( 3–4 ) : 592 – 601 .
  • Spalart , P.R. and Allmaras , S.R. A one-equation turbulence model for aerodynamic flows. In: 30th AIAA Aerospace Sciences Meeting, Reno, NV . AIAA Paper 92-0439 .
  • Sridar , D. and Balakrishnan , N. 2003 . An upwind finite difference scheme for meshless solvers . Journal of Computational Physics , 189 ( 1 ) : 1 – 29 .
  • Steger , J.L. , Dougherty , F.C. and Benek , J.A. 1983 . A chimera grid scheme . Advances in Grid Generation ASME FED , 5 : 59 – 69 .
  • Tang , L. and Yang , J. Hybrid Cartesian grid/gridless algorithm for store separation prediction . AIAA Paper 2010-508, 48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition .
  • Wang , X.Y. 2008 . A SVD-GFD scheme for computing 3D incompressible viscous flows . Computers & Fluids , 37 ( 6 ) : 733 – 746 .
  • Yin , L. , Shen , L. and Lv , G. 2011 . Five-point positive meshless scheme for hyperbolic conservation laws . International Journal for Numerical Methods in Biomedical Engineering , 27 ( 4 ) : 619 – 631 .
  • Yu , P. 2011 . A three-dimensional hybrid meshfree-Cartesian scheme for fluid-body interaction . International Journal of Numerical Methods in Engineering , 88 ( 4 ) : 385 – 408 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.