A mesh-free finite point method for advective-diffusive transport and fluid flow problems

Computational Mechanics

Volumn 21, Issue 4-5, 1998, Pages 283-292

  Onate E ^a   Idelsohn, S ^a,b  

^a INTERNATIONAL CENTER FOR NUMERICAL METHODS IN ENGINEERING CIMNE   (Spain)

^b UNIVERSIDAD NACIONAL DEL LITORAL   (Argentina)

Author keywords

[No Author keywords available]

Indexed keywords

DIFFERENTIAL EQUATIONS; DIFFUSION IN LIQUIDS; INTEGRAL EQUATIONS; INTERPOLATION; LEAST SQUARES APPROXIMATIONS; TRANSPORT PROPERTIES;

ADVECTIVE DIFFUSIVE TRANSPORT; FINITE POINT METHOD (FPM);

HYDRODYNAMICS;

EID: 0032071696     PISSN: 01787675     EISSN: None     Source Type: Journal    
DOI: 10.1007/s004660050304     Document Type: Article

References (39)

1. Babuška I, Melenk JM (1995) The partition of unity finite element method. Technical Note EN-1185, Institute for Physical Science and Technology. Univ. Maryland
2. Batina J (1993) A Gridless Euler/Navier-Stokes solution algorithm for complex aircraft applications. AIAA 93-0333, Reno NV, 11-14 Jan
3. Belytschko T, Lu Y, Gu L (1994) Element free Galerkin methods. Int. J. Num. Meth. Eng. 37:229-56
4. Belytschko T, Organ D, Krongauz Y (1995) A coupled finite-element-element-free Galerkin Method. Comput. Mech. 17:186-195
5. Dolbow J, Belytschko T (1998) An introduction to programming the meshless element free Galerkin Method. In: Arch. in Comp. Meth. in Eng. (in print)
6. p clouds - A meshless method to solve boundary-value problems. TICAM Report 95-05
7. Fischer T (1996) A contribution to adaptive numerical solution of compressible flow problems. Ph.D. Thesis, Universidad Politécnica de Cataluña, Monogr. No. 34, CIMNE, Barcelona
8. Fisher T, Idelsohn I, Oñate E (1995) A meshless method for analysis of high speed flows. AGARD Meeting, Seville
9. Forsythe GE, Wasow WR (1960) Finite Difference Methods for Partial Differential Equations. Wiley, New York
10. Hirsch C (1990) Numerical computations of internal and external flow, Vol. 2. Wiley, New York
11. Hughes TJR, Mallet M (1986) A new finite element formulation for computational fluid dynamics. III: The generalized streamline operator for multidimensional advective-diffusive systems. Comp. Meth. in Appl. Mech. and Eng. 58:305-28
12. Idelsohn S, Oñate E (1994) Finite element and finite volumes. Two good friends. Int. J. Num. Meth. Eng. 37:3323-3341
13. Liszka T (1984) An interpolation method for an irregular set of nodes. Int. J. Num. Meth. Eng. 20:1594-1612
14. Liszka T, Orkisz J (1990) The finite difference method at arbitrary irregular grids and its application in applied mechanics. Comput. Struct. 11:83-95
15. Liu WK, Chen Y (1995) Wavelet and multiple scale reproducing Kernel methods. Int. J. Num. Meth. Fluids 21:901-933
16. Liu WK, Jun S, Zhang YF (1995a) Reproducing Kernel particle methods. Int. J. Num. Meth. Fluids 20:1081-1106
17. Liu WK, Jun S, Li S, Adee J, Belytschko T (1995b) Reproducing Kernel particle methods for structural dynamics. Int. J. Num. Meth. Eng. 38:1655-1679
18. Liu WK, Chen Y, Chang CT, Belytschku T (1996a) Advances in Multiple Scale Kernel Particle Methods. Comput. Mech. 18:73-111
19. Liu WK, Chen Y, Jun S, Chen JS, Belytschko T, Pan C, Uras RA, Chang CT (1996b) Overview and applications of the reproducing Kernel particle methods. Arch. Comput. Meth. in Eng. 3:3-80
20. Liu WK, Hao W, Chen Y, Jun S, Gosz J (1997) Multiresolution Kernel particle methods. Comput. Mech. 20:295-309
21. Lu YY, Belytschko T, Gu L (1994) A new implementation of the element free Galerkin method. Comput. Meth. Appl. Mech. Eng. 113:397-414
22. Mavripilis P, Jameson A, Matinelli L (1989) Multigrid solution of the Navier-Stokes equations on triangular meshes. ICASE Report No. 89-VI, February
23. Moraghan JJ (1988) An introduction to SPH. Comp. Phys. Comm. 48:89-96
24. Nayroles B, Touzot G, Villon P (1992) Generalizing the FEM: Diffuse approximation and diffuse elements. Comput. Mech. 10, 307-18
25. Oñate E (1996) On the stabilization of numerical solution of convective transport and fluid flow problems. Research Report 81 CIMNE, Barcelona, Feb
26. Oñate E (1998) Derivation of stabilized equations for numerical solution of advective-diffusive Transport and fluid flow problems. Comp. Meth. Appl. Mech. Eng., 151:233-265
27. Oñate E, Cervera M, Zienkiewicz OC (1994) A finite volume format for structural mechanics. Int. J. Num. Meth. Eng. 37:181-201
28. Oñate E, Idelsohn S, Zienkiewicz OC (1995a) Finite point methods in computational mechanics. Research Report 67, CIMNE, Barcelona, July
29. Oñate E, Idelsohn S, Zienkiewicz OC, Fisher T (1995b) A finite point method for analysis of fluid flow problems. Proc. 9th Int. Conf. on Finite Element Methods in fluids. Venize, Italy, 15-21 Oct
30. Oñate E, Idelsohn S, Zienkiewicz OC, Taylor RL (1996a) A finite point method in computational mechanics. Applications to convective transport and fluid flow. Int. J. Num. Meth. Eng. 39:3839-3866
31. Oñate E, Idelsohn S, Zienkiewicz OC, Taylor RL (1996b) A stabilized finite point method for analysis of fluid mechanics's problems. Comp. Meth. in Appl. Eng. 139:315-347
32. Oñate E, Garcia J, Idelsohn S (1997) Computation of the stabilization parameter for the finite element solution of advective-diffusive problems. Int. J. Num. Meth. Fluids, 25:1385-1407
33. Peraire J, Peiro J, Formaggia L, Morgan K, Zienkiewicz OC (1988) Finite element Euler computations in three dimensions. Int. J. Num. Meth. Eng. 26:2135-59
34. Perrone N, Kao R (1975) A general finite difference method for arbitrary meshes. Comput. Struct. 5:45-47
35. Taylor RL, Zienkiewicz OC, Idelsohn S, Oñate E (1995) Moving least square approximations for solution of differential equations. Research Report 74, CIMNE, Barcelona, Dec
36. Zienkiewicz OC, Codina R (1995) A general algorithm for compressible and incompressible flow. Part I: The split characteristic based scheme. Int. J. Num. Meth. in Fluids 20:869-85
37. Zienkiewicz OC, Oñate E (1991) Finite elements versus finite volumes. Is there a choice?. In: Wriggers P, Wagner W (eds) Non Linear Computational Mechanics. State of the Art, Springer, Berlin Heidelberg New York
38. Zienkiewicz OC, Taylor RL (1991) The finite element method. Mc Graw Hill, New York
39. Zienkiewicz OC, Morgan K, Satya Sai BVK, Codina R, Vazquez M (1995) A general algorithm for compressible and incompressible flow. Part II: Tests on the explicit form. Int. J. Num. Meth. in Fluids 20:886-913