On the Numerical Solution of Unsteady Fluid Flow Problems by a Meshless Method
Keywords:
Meshless method, diffuse approximation, unsteady fluid flowAbstract
A diffuse approximation method for the solution of time-dependent Navier-Stokes equations is presented. Different preconditioned iterative methods for solving the pressure correction equation are tested. Sample results are presented for the window cavity problem and the fluid flow around a circular cylinder.
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[ALU 01] ALURU N. R., LI G., « Finite cloud method: A true meshless technique based on
fixed reproducing Kernel », International Journal for Numerical Methods in Engineering,
Vol. 50, 2001, pp. 2373-2410.
[BEL 94] BELYTSCHKO T., LU YY., GU L., « Element-free Galerkin methods », International
Journal for Numerical Methods in Engineering, Vol. 37, 1994, pp. 229-256.
[BRE 02] BREITKOPF P., RASSINEUX A. and VILLON P., « An introduction to the moving least
squares meshfree methods », Revue Européenne des Éléments Finis, No 7-8, 2002.
[CHA 01] CHATI M. K., PAULINO G. H., MUKHERJEE S., « The meshless standard and
hypersingular boundary node methods-Applications to error estimation and adaptivity in
the three-dimensional problems », International Journal for Numerical Methods in
Engineering, Vol. 50, 2001, pp. 2233-2269.
[COM 82] COMINI G. and DEL GIUDICE S., « Finite element solution of the incompressible
Navier-Stokes equations », Num. Heat Transfer, Vol. 5, 1982, pp. 463-478.
[COU 98] COUTURIER S., SADAT H., « Résolution des équations de Navier-Stokes dans la
formulation en variables primitives par approximation diffuse », C. R. Acad. Sciences,
t. 326, série IIb, 1998, pp. 117-119.
[DEM 84] DEMKOWICZ L., KARAFIAT A. and LISZKA T., « On some convergence results for
FDM with irregular mesh », Comp. Methods Appl. Mech. Engrg., Vol. 42, 1984, pp. 343-
[JAN 93] JANSSEN R. J. A., HENKES R. A. W. M., « Accuracy of finite-volume discretizations
for bifurcating natural-convection flow in a square cavity », Numerical Heat Tranfer, Part
B, Vol. 24, 1993, pp. 191-207.
[LIU 01] LIU G. R., GU Y. T., « Local point interpolation method for stress analysis of twodimensional
solids », Structural Engineering and Mechanics, Vol. 11, 2001, pp. 221-236.
[OHS 01] OHS R. R., ALURU N. R., « Meshless analysis of piezoelectric devices »,
Computational Mechanics, Vol. 27, 2001, pp. 23-36.
[PAT 80] PATANKAR S. V., Numerical Heat Transfer and Fluid Flow, Hemisphere,
Washington, DC 1980.
[PRA 98] PRAX C., SALAGNAC P. and SADAT H., « Diffuse approximation method and control
volume based finite element methods : a comparative study », Num. Heat Transfer, Part
B, Vol. 34, 1998, pp. 303-321.
[SAA 96] SAAD Y., « Iterative methods for Sparse linear system », PWS, Boston, MA.
[SAD 95] SADAT H., PRAX C., « Résolution des problèmes de mécanique des fluides et de
thermique par approximation diffuse », Congrès de la Société Française des Thermiciens,
Poitiers, mai 1995.
[SAD 96] SADAT S., PRAX C., SALAGNAC P., « Diffuse approximation method for solving
natural convection in porous media », Transport in Porous Media, Vol 22, num. 2, 1996,
pp. 215-223.
[SAD 00] SADAT H. and COUTURIER S., « Performance and accuracy of a meshless method
for laminar natural convection », Numer. Heat Transfer, Part B Fundamentals, Vol. 37,
, pp. 455-467.
[SAI 96] SAIKI E. M., BIRINGEN S., « Numerical simulation of a cylinder in uniform flow:
Application of a virtual boundary method », J. Comput. Phys., Vol. 123, 1996, pp. 450-
[SOP 02] SOPHY T., SADAT H., PRAX C., « A meshless formulation fir three-dimensional
laminar natural convection », Num. Heat Transfer, Part B Fundamentals, Vol. 41, 2002,
pp. 433-445.
[ZHA 00] ZHANG X., SONG K. Z., LU M. W., LIU X., « Meshless methods based on
collocation with radial basis functions », Computational Mechanics, Vol. 26, 2000,
pp. 333-343.
