A meshless method for the solution of incompressible flow equations
Keywords:
diffuse approximation, meshless method, incompressible fluid flow, projection algorithmAbstract
This article reports on the efficiency of a co-located diffuse approximation method coupled with a projection algorithm for the solution of two and three-dimensional incompressible flow equations. Three typical examples show the accuracy of this meshless method.
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References
[ABD 87] ABDALLAH S., « Numerical solutions for the incompressible Navier-Stockes
equations in primitives variables using a non-staggered grid », II, J. Comput. Phys., 70,
p. 193-202, 1987.
[BEL 94] BELYTSCHKO T., Lu Y. Y., GiJ L., « Element free Galerkin methods », Int. J.
Numer. Methods Eng., 37, p. 229-256, 1994.
[BEL 96] BELYTSCHKO T., KRONGAUZ Y., ORGAN D., FLEMING, KRYSL P., «Meshless
methods: an overview and recent developments», Comput. Methods Appl. Mech. Engrg.,
, p. 3-47, 1996.
[COM 82] COMINI G., DEL GIUDICE S., « Finite element solution of the incompressible
Navier-Stokes equations», Numer. Heat Transfer, vol. 5, p. 463-478, 1982.
[COM 94] COMINI G., MANZAN M., NONINO C.,« Finite element solution of the stream
function-vorticity equation for incompressible two-dimensional flows », Int. J. Numer.
Meth. Fluids, vol. 19, p. 513-525, 1994.
[DAT 96] DATE A. W., « Complete pressure correction algorithm for solution of
incompressible Navier-Stokes equations on a nonstaggered grid », Numer. Heat Transfer,
vol. 29, p. 441-458, 1996.
[GHI 82] GHIA U., GHIA K. N., SHIN C. T., « High-Re solutions for incompressible flow
using the Navier-Stokes equations and a multigrid method >>, J. Comput. Phys., vol. 48,
p. 387-411,1982.
[MAS 94] MASSON C., SAABAS H. J., BALIGA B. R., «Co-located equal-order control-volume
finite element method for two-dimensional axisymmetric incompressible fluid flow>>, Int.
J. Numer. Meth. Fluids, vol. 18, p. l-26, 1994.
[MEL 93] MELAAEN M. C.,« Nonstaggered calculation of laminar and turbulent flows using
curvilinear nonorthogonal coordinates >>, Numer. Heat Transfer, Part A, vol. 24, p. 375-
, 1993.
[NAY 91] NAYROLES B., TOUZOT G., VILLON P., «The diffuse approximation>>, C. R. Acad.
Sci. Paris, Serie II, 313, p. 133-138, 1991.
[NOB 96] NOBILE E.,« Simulation of time-dependent flow flow in cavities with the additivecorrection
multigrid method, Part II : Applications », Numer. Heat Transfer, Part A,
vol. 30, p. 351-370, 1996.
[NON 97] NONINO C., COMINI G., « An equal-order velocity-pressure algorithm for
incompressible thermal flows». Part I and Part 2, Numer. Heat Transfer, vo!. 32, p. 1-35,
[PRA 85] PRAHASH C., PATANKAR S.V., «A control-volume based finite-element method for
solving the Navier-Stokes equations using equal-order velocity-pressure interpolation »,
Numer. Heat Transfer, vo!. 8, p. 259-280, 1985.
[SAD 96] SADAT H., PRAX C.,« Application of the diffuse approximation for solving fluid
flow and heat transfer problems», Int. J. Heat Mass Transfer, vo!. 39, no. 1, p. 214-218,
[SOH] SOHN J.L.,« Evaluation of FIDAP on some classical laminar and turbulent bench
marks», Int. J. Numer. Meth. Fluids, vol. 8., p. 1469-1490, 1994.
[TAN 95] TANG L. Q., CHENG T., TSANG T. T. H., « Transient solutions for the three
dimensional lid-driven cavity by a least-squares finite element method », Int. J. Numer.
Meth. Fluids, vol. 21, p. 413-432, 1995.
[TAY 81] TAYLOR C., HUGHES T.G., Finite element programming of the Navier-Stokes
equations, Pineridge Press, Swansea, UK, 1981.
[TRO 85] TROPEA C. D., GACKSTATTER R., « The flow over two-dimensional surfacemounted
obstacles at low Reynolds numbers », J. Fluids Eng., vol. 107, p. 489-494,