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Paul August 3, 1998 09:52

Gridless methods

I am interested in finding out recent work on Gridless Methods in CFD. Could someone give me reference to books/papers on this subject.

Thanks a lot.


Farid Moussaoui August 3, 1998 11:36

Re: Gridless methods

I think that meshless=gridless. So I propose this references that Prof Cord Rossow from DLR gave me.

Fischer,T.; Onate,E.; Idelsohn,S. A meshless technique for computer analysis of high speed flows AGARD Symposium on Progress and Challenges in CFD Methods and Algorithms, 1995

Liu,J.L., Su,S.j. A potentially gridless solution method for the compressible Euler/ Navier-Stokes equations AIAA Paper 96-0526, 1996

Duarte,C.A., Oden,J.T. Hp Clouds - a meshless method to solve boundary-value problems TICAM-report 95-05, 1995

Adrin Gharakhani August 13, 1998 21:29

Re: Gridless methods
If you're looking for grid-free solutions in the incompressible flow regime, your best bet is to look into vortex-based methods.

New developments in 2D vortex methods show that the solutions are spectrally accurate at a fraction of the cost (and memory) of spectral element methods for high Reynolds numbers:

1:PhD Thesis by Shankar Subramaniam:A new mesh-free vortex method, the Florida state university, 1996

2:S. Shankar and L. van Dommelen, A new diffusion procedure for vortex methods, JCP, vol 127, 88-109, 1996.

3D vortex solutions of wall bounded flows are at their infancy but some significant progress has been made in recent years:

1:A. Gharakhani & A. F. Ghoniem, Three-Dimensional Vortex Simulation of Time Depenedent Incompressible Internal Viscous Flows, JCP, Vol 134, 75-95, 1997 with good references to others' works,

2:A. Gharakhani & A. F. Ghoniem, Simulation of the Piston Driven Flow Inside a Cylinder with An Eccentric Port, JFE, Vol 120, 319-326, 1998

3:A. Gharakhani & A. F. Ghoniem, 3D Vortex Simulation of Flow In Engines During Compression, ASME 1998 Summer Fluids Eng. Conference, Wash. DC

For compressible flows the SPH method has been in use for some time now:

1: J.J. Monaghan, An Introduction to sph, Comp. Phys. Comm., vol 48, 89, 1998

More recently, the finite element community has made some significant progress in grid-free methods for incompressible as well as compressible flows (Oden et al were referenced by others) For a decent reference for these types of methods check:

1:C. A. Duarte & J. T. Oden, H-p Clouds - An h-p Meshless Method, Numer. Methods for Partial Differential Equations, Vol. 12, 673-705, 1996

Adrin Gharakhani, Sc.D. - Applied Scientific Research

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