Dear Yang

many thanks for this Q.

Dear colleagues please add my question to the above

it seems that solving a matter via mesh free methods may be dependent to your initial guess and moreover may converge to an answer which is just mathematically true while it is not real answer.

is this statement true?

regards

Hi,

Maybe this tutorial a liitle bit could help you, I also are struggling in my design project using CFD.

Can go through the blog: http://learncax.com/blog/by-category/cfd/no-meshing-its-meshless-cfd

you can read the excellent Toro's book on finite volume methods (what is behind CFD) :

http://mmc2.igeofcu.unam.mx/luiggi/MMC/Leveque.pdf

And also the very good free CLAWPACK from Levesque :

http://www.clawpack.org/

Prof SM Deshpande (IISc/JNCASR, Bangalore,India) and his co-workers have done extensive work in meshfree methows. You can google SM Deshpande and get a good number of references.

Dear Kishore Kumar Sankara, thanks for give me this useful infomation. But in China, we cannot use Google, so could you please tell me the title of the paper you mentioned? Thank you.

There are various groups who been working on meshfree methods. Have a look here for instance;

http://onlinelibrary.wiley.com/doi/10.1002/fld.3698/abstract

http://cfd4aircraft.com/pub_files/AIAA-2013-0867.pdf

Thanks，Sebastian Timme 

Here are some.Some publications of Prof Deshpande can be found at

http://www.jncasr.ac.in/smd/publication.php

Some by Dr Ramesh are listed below

Smac mimetics increase cancer cell response to chemotherapeutics in a TNF-α-dependent manner

BL Probst, L Liu, V Ramesh, L Li, H Sun, JD Minna, L Wang

Cell Death & Differentiation 17 (10), 1645-1654

59 2010

Least squares grid free kinetic upwind method

V Ramesh

Indian Institute of Science, Bangalore

24 2002

Theory and application of 3-D LSKUM based on entropy variables

SM Deshpande, K Anandhanarayanan, C Praveen, V Ramesh

International journal for numerical methods in fluids 40 (1-2), 47-62

18 2002

Least squares kinetic upwind method on moving grids for unsteady Euler computations

V Ramesh, SM Deshpande

Computers & fluids 30 (5), 621-641

13 2001

Unsteady flow computations for flow past multiple moving boundaries using LSKUM

V Ramesh, SM Deshpande

Computers & Fluids 36 (10), 1592-1608

11 2007

Low dissipation grid free upwind kinetic scheme with modified CIR splitting

V Ramesh, SM Deshpande

Fluid Mechanics Report

10 2004

Euler computations on arbitrary grids using LSKUM

V Ramesh, SM Deshpande

Computational Fluid Dynamics 2000, 783-784

8 2001

Kinetic treatment of the far-field boundary condition

V Ramesh, JS Mathur, SM Deshpande

Fluid Mechanics Report 97

8 1997

q-LSKUM-A new higher order kinetic upwind method for euler equations using entropy variables

MZ Dauhoo, AK Ghosh, V Ramesh, SM Deshpande

Computational Fluid Dynamics Journal 9 (1)

6 2000

q-LSKUM-A new higher order kinetic method for Euler equations using entropy variables

MZ Dauhoo, AK Ghosh, V Ramesh, SM Deshpande

Proceedings ISCFD 99

6 1999

Least squares kinetic upwind method with modified CIR splitting

V Ramesh, SM Deshpande

7th AeSI CFD symposium

5 2004

Navier-Stokes analysis of GA (W)-2 aerofoil with deflected flap and redesign of HANSA flap for better performance

SK Chakrabartty, K Dhanalakshmi, V Ramesh

Computational Fluid Dynamics Journal 12 (1), 89-97

3 2003

Navier-Stokes analysis and design of aerofoil-flap configurations for low speed aircraft

SK Chakrabartty, K Dhanalakshmi, V Ramesh

Computational Fluid Dynamics Journal 11 (3), 285-289

2 2002

Adaptive Cloud Refinement (ACR)-Adaptation in Meshless Framework

M Somasekhar, S Vivek, KS Malagi, V Ramesh, SM Deshpande

Communications in Computational Physics 11 (4), 1372-1385

1 2012

Efficient cloud refinement for kinetic meshless methods

M Somasekhar, S Vivek, KS Malagi, V Ramesh, SM Deshpande

Meshfree Methods for Partial Differential Equations V, 207-217

1 2011

Kinetic meshless methods for unsteady moving boundaries

V Ramesh, S Vivek, SM Deshpande

Meshfree Methods for Partial Differential Equations V, 189-206

1 2011

Convergence acceleration of mesh-less Euler solver

MK Singh, V Ramesh, N Balakrishnan

12th Annual CFD Symposium

1 2010

Mesh less Euler Computation for Cropped Delta Wing with Aileron Deflection

MK Singh, V Ramesh, SM Deshpande

1 2009

Grid free euler computations using modified cir splitting

V Ramesh, JS Mathur, SM Deshpande

1 2007

Unsteady computations for flow past two oscillating airfoils

V Ramesh, SM Deshpande

1 2006

It is not really a Mesh-free method, but can help you to avoid time costly and complicated Mesh generation. The CFD solver CONVERGE basically creates a cartesian mesh over a chosen geometry and refines it automatically in the regions of high gradients of pressure, velocities, species concentration etc. I have used it for the calculations of internal combustion engines and the results we of physically high quality.

You can read first some good books on mesh free methods :

An introduction to mesh free methods and their programming by G.R LIU and Y.t GU

Smoothed Particle Hydrodynamics: A Meshfree Particle Method by G. R. Liu, M. B. Liu

Fluid Mechanics and the SPH Method

Theory and Applications

Damien Violeau

http://www.ccms.ac.cn/wangfz/An%20Introduction%20to%20Meshfree%20Methods%20and%20Their%20Programming.pdf

https://global.oup.com/academic/product/fluid-mechanics-and-the-sph-method-9780199655526?cc=fr&lang=en&

dear Pascal GALON ，thanks very much for giving me so much useful information. 

https://www.researchgate.net/publication/297245624_Particle_Swarm_Optimization_Algorithm_and_its_Codes_in_MATLAB

Research Particle Swarm Optimization: Algorithm and its Codes in MATLAB

https://www.researchgate.net/publication/296636431_Codes_in_MATLAB_for_Particle_Swarm_Optimization

Code Codes in MATLAB for Particle Swarm Optimization