Publication Cover
Numerical Heat Transfer, Part B: Fundamentals
An International Journal of Computation and Methodology
Volume 51, 2007 - Issue 5
64
Views
7
CrossRef citations to date
0
Altmetric
Original Articles

An Introduction to the Lattice Grid

, , , &
Pages 415-431 | Received 24 Jun 2006, Accepted 22 Nov 2006, Published online: 14 May 2007

REFERENCES

  • D. W. Zingg , Comparison of High-Accuracy Finite-Difference Methods for Linear Wave Propagation , SIAM J. Sci. Comput. , vol. 22 , pp. 476 – 502 , 2000 .
  • J. R. Pacheco and R. E. Peck , Nonstaggered Boundary-Fitted Coordinate Method for Free Surface Flows , Numer. Heat Transfer B , vol. 37 , pp. 267 – 291 , 2000 .
  • W. Z. Shen , J. A. Michelsen , and J. N. Sorensen , A Collocated Grid Finite Volume Method for Aeroacoustic Computations of Low-Speed Flows, J. Comput. Phys. , vol. 196, pp. 348–366, 2004.
  • D. C. Lo , D. L. Young , and Y. C. Lin , Finite-Element Analysis of 3-D Viscous Flow and Mixed-Convection Problems by the Projection Method , Numer. Heat Transfer A , vol. 48 , pp. 339 – 358 , 2005 .
  • J. R. Pacheco , A. Pacheco-Vega , T. Rodic , and R. E. Peck , Numerical Simulations of Heat Transfer and Fluid Flow Problems Using an Immersed-Boundary Finite-Volume Method on Nonstaggered Grids , Numer. Heat Transfer B , vol. 48 , pp. 1 – 24 , 2005 .
  • Y.-Y. Tsui and Y.-F. Pan , A Pressure-Correction Method for Incompressible Flows Using Unstructured Meshes , Numer. Heat Transfer B , vol. 49 , pp. 43 – 65 , 2006 .
  • C. W. Hirt , A. A. Amsden , and J. L. Cook , An Arbitrary Lagrangian-Eulerian Computing Method for All Flow Speeds , J. Comput. Phys. , vol. 14 , pp. 227 – 253 , 1974 .
  • J. B. Bell , P. Colella , and H. M. Glaz , A Second-Order Projection Method for the Incompressible Navier-Stokes Equations , J. Comput. Phys. , vol. 85 , pp. 257 – 283 , 1989 .
  • J. Zhu and J. A. Sethian , Projection Methods Coupled to Level Set Interface techniques , J. Comput. Phys. , vol. 102 , pp. 128 – 138 , 1992 .
  • F. H. Harlow and J. F. Welch , Numerical Calculation of Time-Dependent Viscous Incompressible Flow of Fluid with Free Surface , Phys. Fluids , vol. 8 , pp. 2182 – 2189 , 1965 .
  • S. Nagarajan , S. K. Lele , and J. H. Ferziger , A Robust High-Order Compact Method for Large Eddy Simulation , J. Comput. Phys. , vol. l91 , pp. 392 – 419 , 2003 .
  • M.-J. Ni , S. Komori , and N. Morley , Projection Methods for the Calculation of Incompressible Unsteady Flows , Numer. Heat Transfer B , vol. 44 , pp. 533 – 551 , 2003 .
  • M.-J. Ni , M. Abdou , and S. Komori , A Variable-Density Projection Method for Interfacial Flows , Numer. Heat Transfer B , vol. 44 , pp. 553 – 574 , 2003 .
  • M. Piller and E. Stalio , Finite-Volume Compact Schemes on Staggered Grids , J. Comput. Phys. , vol. 197 , pp. 299 – 340 , 2004 .
  • X.-Y. Luo , M.-J. Ni , A. Ying , and M. A. Abdou , Numerical Modeling for Multiphase Incompressible Flow with Phase Change , Numer. Heat Transfer B , vol. 48 , pp. 425 – 444 , 2005 .
  • K. K. Q. Zhang , W. J. Minkowycz , and F. Mashayek , Exact Factorization Technique for Numerical Simulations of Incompressible Navier-Stokes Flows , Int. J. Heat Mass Transfer , vol. 49 , pp. 535 – 545 , 2006 .
  • M.-J. Ni , Projection and Simple Methods for Single-Fluid and Multiple-Fluid Incompressible Unsteady Flows General Formula , Numer. Heat Transfer B , vol. 50 , pp. 395 – 408 , 2006 .
  • K. K. Q. Zhang , B. Shotorban , W. J. Minkowycz , and F. Mashayek , A Compact Finite Difference Method on Staggered Grid for Navier-Stokes Flows , Int. J. Numer. Meth. Fluids , vol. 52 , pp. 867 – 881 , 2006 .
  • I. Babuska , Error Bounds for Finite Element Method , Numer. Math. , vol. 16 , pp. 322 – 333 , 1971 .
  • Y. Morinishi , T. S. Lund , O. V. Vasilyev , and P. Moin , Fully Conservative Higher Order Finite Difference Schemes for Incompressible Flow , J. Comput. Phys. , vol. 143 , pp. 90 – 124 , 1998 .
  • P. M. Gresho and R. L. Sani , Incompressible Flow and the Finite Element Method , Wiley , New York , 2000 .
  • D. A. Kopriva and J. H. Kolias , A Conservative Staggered-Grid Chebyshev Multidomain Method for Compressible Flows , J. Comput. Phys. , vol. 125 , pp. 244 – 261 , 1996 .
  • B. Alder , S. Fernbach , and M. Rotenburg , Computational Design of the Basic Dynamical Processes of the UCLA General Circulation Model , Meth. Comput. Phys. , vol. 17 , p. 173 , l977 .
  • J. Kim and P. Moin , Application of a Fractional-Step Method to Incompressible Navier-Stokes Equations, J. Comput. Phys. , vol. 59, pp. 308–323, 1985.
  • S. L. Zhang . GPBi-CG: Generalized Product-Type Methods Based on Bi-CG for Solving Nonsymmetric Linear Systems , SIAM J. Sci. Comput. , vol. 18 , pp. 537 – 551 , 1997 .
  • S. Fujino , GPBiCG(m,l): A Hybrid of BiCGStab and GPBiCG Methods with Efficiency and Robustness , Appl. Numer. Math. , vol. 41 , pp. 107 – 117 , 2002 .
  • U. Ghia , K. N. Ghia , and C. T. Shin , High-Re Solutions for Incompressible Flow Using the Navier-Stokes Equations and a Multigrid Method , J. Comput. Phys. , vol. 48 , pp. 387 – 411 , 1982 .

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.