I am currently working on simulation fluid flow including the solidification in molding process.I will be so thankful if someone guide me to find any upwinding methods or any information about upwindig method for analysing aboved modeling.

thanx s.afkhami

Are you looking to use high resolution methods or front tracking methods? I.e. How accurate do you want to solve for your solidification front.

HIGH ACCURACY--> FRONT TRACKING (diffuses w/ 1 cell)

Med. ACCURACY--> High Resolution (TVD,MUSCL,etc...)

(diffuses w/ 2-3 cells)

A good start is to read "Numerical Methods for Conservation Laws" by R. LeVeque. Check out his homepage and you will find some useful software and links there as well. This might help too...

"Kothe, D. and Juric, D. and Lam, K. and Lally, B.", "1998", Numerical Recipes for mold filling simulation, Proceedings of the Eighth International conference on modeling and casting, welding, and advanced solidification processes}

Hope this helps......

Schemes based on the Volume of Fluid (VOF) method are very useful for solving the kind of problems you are looking at. Recent VOF methods use multi-dimensional upwinding based on reconstruction of domain of dependencies. These methods have been around for a while but you can look at recent papers on the subject in the Journal of Comp. Phys. (some of the authors : Rider, Kothe, Puckett)

There is also the phase field method based on free-energy optimization that is often used for modeling dendritic growth in flows with phase change. I am not sure of it's numerical implementation but I am sure you have some kind of upwinding in it. You can find a recent review in the Annual Review of Fluid Mechanics (with the phrase "Diffuse Interface Method" in the title of the paper).

I don't know the method you will use (FVM, FEM...), front tracking, enthalpy, capacitance, etc. but I have a few references:

1) V.R. Voller, Solidification, Computational methods for free and moving and Boundaries, (sorry I d'ont have the year nor the editor)

2) V.R. Voller and A.D. Brent and C.Prakash. The modelling of heat, mass and solute transport in solidification systems. I.J. Heat and Mass transfer Vol 32 No9 pp1719-1731, 1989

Look for V.R. Voller, he wrote numerous articles on the subject.

3) K.O'Neill, Boundary integral equation solution of moving boundary phase change problems. I.J for numerical methods in engineering vol19 1825-1950 (1983)

4) M.Lacroix and A.Gagnon, Numerical Solution oh phase change problems, an Eulerian-Lagrangian approach. Numerical heat transfer Part B, vol 19 pp57-78 (1992)

5) D. Lynch, K.O'Neill. Continuously deforming finite elements for the solution of parabolic problems, with and without phase change. I.J. for numerical methods in engineering vol 17 81-96 (1981).

Tomorrow, I have a the time I could give you a few more references.