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Old   January 3, 2008, 07:29
Default meshless
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I am looking for the references of the first papers dealing with meshless methods applied to heat transfer and fluid flow problems.
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Old   January 3, 2008, 08:14
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jinwon park
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See T.G. Liu 'smoothed particle hydrodynamics'
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Old   January 3, 2008, 14:52
Default Re: meshless
Praveen. C
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Here is a list of some references you might find useful

1. T Liszka, "An interpolation method for an irregular net of nodes", Int. Jl. for Num. Meth. in Engg., 20:1599-1612, 1984.

2. T Liszka and J Orkisz, "The finite difference method at arbitrary irregular grids and its application in applied mechanics'', Comp. Struct., 11:83-95, 1980.

3. KC Chung, "A generalised finite difference method for heat transfer problems of irregular geometries'', Num. Heat Transfer, 4:345-357, 1981.

4. EJ Kansa (1990): "Multiquadrics- A scattered data approximation scheme with applications to computational fluid dynamics: II. Solutions to parabolic, hyperbolic and elliptic partial differential equations", Comput. Math. Appl., 19(6-8):147-161.

5. JT Batina, "A gridless Euler/Navier-Stokes solution algorithm for complex aircraft applications'', AIAA Paper 93-0333, 1993.

6. T Belytschko, YY Lu, and L Gu, "Element-free Galerkin methods", Int. Jl. Num. Meth. Engg., 37:229-256, 1994.

7. AK Ghosh, SM Deshpande, "Least squares kinetic upwind method for inviscid compressible flows'', AIAA paper 95-1735,1995.

8. Yagawa G and Yamada T, "Free mesh method: A new meshless finite element method'', Comp. Mech., 18:383-386, 1996.

9. T Belytschko, Y Krongauz, D Organ, M Flemming and P Krysl, "Meshless methods: An overview and recent developments", Comput. Methods Appl. Mech. Engg., Vol. 139, pp. 3-47, 1996.

This contains a comprehensive review of many meshless techniques.

10. K Morinishi (1999): "An implicit gridless type solver for the Navier-Stokes equations'', Int. Symp. on CFD, Bremen.

11. H Wendland (1999): "Meshless Galerkin methods using radial basis functions", Math. Comp., 68:1521-1531.

12. M Junk, "Do finite volume methods really need a mesh ?", Int. Workshop on Meshfree Methods for PDE, Bonn, September, 2001.

13. R Lohner, C Sacco, E Onate and S Idelsohn (2002): "A finite point method for compressible flows'', Int. Jl. Num. Meth. Engg., Vol. 53, pp. 1765-1779.

14. Michael Griebel and Marc Schweitzer, ed. (2002): Meshfree methods for Partial Differential Equations, LNCSE, Springer, 2002.

15. G.R. Liu: Meshfree Methods - Moving beyond the Finite Element Method , 712 pages, 2002, CRC Press. ISBN: 0849312388

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Old   January 3, 2008, 15:33
Default Re: meshless
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just add this: there is a good review paper by J.J. Monaghan (inventor of SPH) which is worth to notice (if you have not access give ur email, i have e-copy):

J J Monaghan, Smoothed Particle Hydrodynamics, Annual Review of Astronomy and Astrophysics, 1992, Vol. 30, Pages 543-574

Also, i would like to draw your attention to an attractve branch of meshless methods based on R-function (semi analytical geometry) and distance filed (with exact satisfaction of boundary condition unlike othetr meshless methods that suffer from bc issue), works by Vadim Shapiro, Igor Tsukanov and V. Rvachev, e.g. see:

Field modeling with sampled distances, Computer-Aided Design 38, 87"100, 2006.

The architecture of SAGE: A meshfree system based on RFM, Engineering with Computers 18, 295"311, 2002

Meshfree simulation of deforming domains, Computer-Aided Design 31, 459"471, 1999

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Old   January 3, 2008, 17:48
Default Re: meshless
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I would suggest reading thesis of Chaniotis, A. :

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