FINITE VOLUME METHODS for NONOrthogonal Grids
Please help.
I'm writing code for FVM on a nonorthogonal grids. Main difficulty  discretization of the convective, diffusion and source terms of the transport equation on a nonorthogonal mesh. I found some description in Joe F. Thomson Grid Book, in some theses and articles, but it's not enough. Please help. I've spent three whole days and sleepless nights in Google, AltaVista, Yandex and without result. I'm desperate. I promise, that in my CFD thesis I'll describe this question in smallest details and will place my thesis in Internet, in order that fellows like me could work without such difficulties. PLEASE...... 
Re: FINITE VOLUME METHODS for NONOrthogonal Grids
My dear friend,
There is plenty of literature out ther on this subject. Start with the book of Peric and Muzaferija. Have look through the thesis of Hrvoje Jasak (the link is somehwere in these threads) Just search for Jasak. He and mr Peric are the GURUS of this field. Let me just add that you are now involving yourself with the cutting edge of CFD! This is the way forward for CFD. Let there be no doubt about it!!! Happy modelling! 
Re: FINITE VOLUME METHODS for NONOrthogonal Grids
I have answered this in your earlier thread.
If you really have spent 3 days and got nowhere I would strongly suggest you find someway to get some supervision. It would take any supervisor familiar with numerical methods about a minute to point you in the right direction. Failing that, I would recommend reading covertocover a reasonable CFD book before attempting to write any code. There are some on the internet. I would also strongly recommend downloading one of the available CFD codes and reading it "covertocover". Run the code to check it does what your expect. Then start your coding by modifying it for your purposes. No rational supervisor would ask one of their new student to write a code from scratch. (And this is a supervised student!) They would give them a code to learn from. Later, if necessary, a fresh code might be written but it is rarely necessary. 
Re: FINITE VOLUME METHODS for NONOrthogonal Grids
Dear Jonno, thank You,
I send an Email to Mr. Hrvoje Jasak, asking him to allow me to copy of his Ph.D. Thesis. If he will be kind to me, I will get it. I am too shy to disturb people, all I can do  to search in Internet and send question at CFDonline. I haven't connections with any of powerful people in CFD and still work by myself. Do You know more issues about nonorthogonality which can be downloaded for free? I found a lot, but it's not that suit me. Below I listed manuals of CFD codes, where I could find description of the problem, but .... Manuals: 1) CALCPVM: A Parallel SIMPLEC Multiblock Solver for Turbulent Flow in Complex Domains by Hakan Nilsson and Lars Davidson 2) CALCBFC: A FiniteVolume Employing Collocated Variable Arrangement and Cartesian Velocity Components for Computation of Fluid Flow and Heat Transfer in Complex ThreeDimensional Geometries by Lars Davidson and Bijan Farhanienh 3) ISAAC version 4.2. by Joseph H. Morrison 4) ISNaS  the Deft incompressible flow solver by Guus Segal, Marcel Zijlema, Ronald van Nooyen, Charles Moulinec, version 1.1 5) STREAM Version 4.5.2 6) caffa3d.MB A fully implicit, finite volume, flow solver for the incompressible 3D NavierStokes equations with generic scalar transport, in block structured, nonorthogonal, body fitted grids by Gabriel Usera 7) RELAX3D  program for solving 2 and 3dimensional Laplace and Poisson equations 8) SPARC – Structured PArallel Research Code by Franko Magagnato 9) Fluent descriptiom 10) PHOENICS description 11) MFIX by Madhava Syamlal 12) NaSt3DGP description Also I can list links to courses of CFD which I found, but there is not description which I need. 
Re: FINITE VOLUME METHODS for NONOrthogonal Grids
Andy thank You very much for Your advice
I also think that it would be better if I had supervisor. There are only three men who helped me:  E.M.Smirnov from St.Petersburg Technical University, he wrote a recommendation letter to Mr. Gunnar Johansson,  Jonas Larsson who encourage me to apply to Chalmers  Gunnar Johansson, he send me an invitation to participate in International Masters Progarm in Turbulence at Chalmers. They are too busy to help me in such questions. I suppose it's difficult to find supervisor, who would agreed to spend his time for unknown and remote student, besides who doesn't pay money. I hope that finally I will resolve all contradictions, and finally aplly for Master's degree somewhere either to Chalmers or to KTH. Here I have a lot to do: basic knowledge of fluid and gas dynamics, fundamentals of CFD, Maple, MATLAB, TEX It will take at least an year. I can list links to a lot of CFD courses (course notes, handouts, lectures) wich I found. And I can say that it's more than sufficient. Buying books is too expensive for me, and thanks to God there is an Internet. When I finish my thesis I'll write free CFD book which I place in Internet, in order that no one suffer like I 
Re: FINITE VOLUME METHODS for NONOrthogonal Grids
drop me an email, i will try to help you with this. (i am very busy now a days but i think in this regard i could be help)

Re: FINITE VOLUME METHODS for NONOrthogonal Grids
This paper might be useful.
Multigrid acceleration for recirculating laminar and turbulent flows computed with a nonorthogonal, collocated finitevolume scheme Computer Methods in Applied Mechanics and Engineering (ISSN 00457825), vol. 118, no. 34, p. 351371 Harish 
Re: FINITE VOLUME METHODS for NONOrthogonal Grids
Andy many thanks, for that, I just discover Your responce. I looked through Thomas H. Pulliam's VKI lectures notes, but unfortunately it's not that I would like to see. I need implementation for FiniteVolume application.
Anyway great thanks for Your help and support. It depends on: (1) what coordinates system you use to express the velocity/tensor components of your solution variables. Cartesian components are common but grid orientated components can have advantages. (2) what coordinate system you use to express the spatial derivatives. For a structured grid this would usually be a coordinate system based on the grid because it is easy to evaluate. (3) which independent coordinate directions you choose to decompose the vector/tensor components of the solution variables. This usually follows from (1) but with the occasional exception. The most common choice is: (1) Cartesian, (2) grid orientated, (3) Cartesian. This is also perhaps the easiest since one can derive all the terms in the NavierStokes equations without needing to get to grips with coordinate systems and tensor analysis. All you need is the chain rule of differentation to expand the Cartesian spatial derivatives in terms of the grid coordinates and Cramers rule (or equivalent) to replace terms like di/dx with a combination of terms like dx/di which can be evaluated on the grid. If I recall correctly, the Introduction to CFD VKI course notes of Anderson have a worked tutorial of the approach. This course ran for many years and the notes are widespread but I do not if they are on the internet. Tom Pulliam's CFD course notes have the Jacobian flux matrices in the Appendices which you should find useful. These are on the internet somewhere. His 2D CFD code is freely available. I think his 3D code is only freely available to Americans but I could be wrong. Whatever, I am sure it is on his home page or somebodies homepage somewhere. He also wrote quite a good CFD book along with a couple of others which is available on the internet somewhere. Can anybody firm up my wobbly references? 
Re: FINITE VOLUME METHODS for NONOrthogonal Grids
I still complete fool in such questions. I collected a lot of literature, printed all Numerical Grid generation by Joe F. Thomson & Z.U.A.Warsi (it lies on my table in front of me), but I still can not understand, how to derivate equation for convective and diffusion fluxes through cell face for FV in curvilinear coordinates.

Re: FINITE VOLUME METHODS for NONOrthogonal Grids
Many thanks Harish, I found it
http://www.elsevier.com/wps/find/jou...on#description , but to have an article it's necessary to pay. I'm out of money. If Your have scanner, please send a copy of it in any graphical form .gif, .jpg or any other Mike 
Re: FINITE VOLUME METHODS for NONOrthogonal Grids
I got the paper from scholar search option in google and I do not have access to that paper either :(.
Harish 
Re: FINITE VOLUME METHODS for NONOrthogonal Grids
Your email does not accept the file that i send because it seems that the size was huge. Gimme another account where i can send the file
Harish 
Re: FINITE VOLUME METHODS for NONOrthogonal Grids

Re: FINITE VOLUME METHODS for NONOrthogonal Grids
Dear HARISH GOPALAN
Thank You very much for Your help and support But OE (in OutLook Express) removed access to the attachment If it won't be very difficult to You, please, rename it to the .txt and send again. Great Thanks Michail 
Re: FINITE VOLUME METHODS for NONOrthogonal Grids
go to mail.yahoo.com and login with your id and password and download it.
H 
Re: FINITE VOLUME METHODS for NONOrthogonal Grids
I try but I can't. After OutLook Express it dissapeared from Yahoo.

Re: FINITE VOLUME METHODS for NONOrthogonal Grids
The finite volume method is designed from the beginning to deal with volumes of any shape, the mesh does not have to be orthogoal, structured or any other limitation, all these limitations need clever coding and the data structure has to cope with this opennness. I am not sure if you are talking about the finite volume method or something else. For information about the finite volume method, read the following book: Computational Fluid Dynamics, Principles and Applications By J. Blazek Published by Elsevier.

Re: FINITE VOLUME METHODS for NONOrthogonal Grids
Dear Ahmed
Thank You for Your response. I indeed talk abot FVM. Main difficulty: how make discretization of general transport equation on a nonorthogonal grid, in general curvilinear boundary fitted coordinates. how to derive equations for 1) surface area 2) convective fluxes 3) diffusion fluxes There is some description in Joe Thomson's "Grid generation" book, but it rather complicated, and difficult for understanding. Besides I never use only one issue for getting information. In vector notation its rather difficult to understand. I have some experience and know that all must be in conservative form. There is some description in Lars Davidson's work "Flux2D A FiniteVolume Computer program written in general NonOrthogonal Coordinates for Calculationof twodimensional flow" BUT. There is only for 2D case, but I would like to have generalization for 3D case. Also I don't like manner of description. Will be very pleased if You can help ANy freedownloadable references are very welcome 
Re: FINITE VOLUME METHODS for NONOrthogonal Grids
I gave you the name of the only book I know of where all your questions are already answered. As you understand it, I cannot scan any copyrighted material, but the book is well worth the money you pay for it. Good luck with your project, it takes a year to develop that but you will end up with another FLUENT

Re: FINITE VOLUME METHODS for NONOrthogonal Grids
Dear Ahmed, thank You a lot for Your help.
What is the name of the book? About project. I am going to rewrite codes by Peric and caffa3D and develop free code for educational/not very serious research purposes in FORTRAN. It will be a good practice for me and good for CFD community. I don't mind that it will take an year or may be even more, I have all my life in the future I have nothing to hurry to. Till I have to be in Lithuania with my mom I will work. Then I hope to join one of universities, preferably KTH or Chalmers. So we will see what I will do. Thank You for Your help. Waiting for the name of book You recommended 
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