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Marcio Aredes Martins December 10, 1999 23:22

Unstructured Finite Volume Method
I possess the formation in Finite Elements Methods and now I began a study on the Finite Volume Method in triangular meshes. In this study, initially, I have interest in solving the 2D steady-state Laplace equation.

I would be amazed if someone were able to me to indicate a reference that presents with more details the discretization and application of boundary conditions for the Laplace equation, to future CFD aplications.

At once I thank the attention,

Marcio Arêdes Martins, MSc

Chemical Engineering

Doctoral Student - Mechanical Department

Universidade Federal de Minas Gerais - Brazil

John C. Chien December 11, 1999 00:23

Re: Unstructured Finite Volume Method
(1). David Creech has professionally compiled a very complete list of CFD related books, and it can be found in the CFD-online's resources section (/resources/documents/books online/CFD literature). (2). For some, the books are expensive. But I think,you can get your school library to buy the book first. (3). It is always hard to say which book is better for you. The guideline is to briefly go through the book and decide whether it match your background, and don't try to read a book which is above your background. If you read enough books, somewhere along the line, you will get your answer. (for example, to study windows and C++, I have studied over 30 books on my own.) (4). What you need is the direction, and David Creech has made it easier for you. If you are looking for CFD related books, visit David's CFD literature section first.

Morteza Marivani December 15, 1999 04:12

Re: Unstructured Finite Volume Method
you can find some information in following papers:

1. unstructured mesh quality assessment and upwind Euler

solution algorithm validation.

Journal of aircraft

vol 31, No 3, May-June 1994 2. Unsteady Euler aifoil solutions using unstructured dynamic meshes

AIAA,Vol 28, No 8, August 1990 3.Unstructured grid generation and simple triangulation algorithm for arbitrary 2-D geometries using object oriented programming . international journal for numerical methods in enineering, vol 40, 251-268,1997

also ,one of the students od Dr. Karim Mazaheri has done this work exactly. Dr. Karim Mazaheri teaches in the sharif University of technology. Also, there is a paper about this subject, but unfortunately, it is in farsi.

Fabio Saltara January 7, 2000 18:00

Re: Unstructured Finite Volume Method
Try the book "Transferência de calor e mecânica dos fluidos computacional", Clóvis maliska, LTC editora

Marcio Aredes Martins January 7, 2000 21:23

Re: Unstructured Finite Volume Method
Dear Fabio Saltara

I really know the Maliska's book, in fact I made the course of Finite Volume Method in this. In fact two methodologies are presented in this, one using the voronoi diagram associated to the Delaunay triangularization, and other called of CVFEM (Control Volume Finite Element Method) originally formulated by Partankar. The disadvantage of the voronoi diagram is that not always it is possible to build a mesh composed by Delaunay triangles. The method CVFEM is an extension of the voronoi diagram, but it is absent of the ortogonality propertie. It uses the finite element SHAPE FUNCTION for the requested interpolation. A priori, these methods work well. The problem is that, in fact, the triangle is not used in the discretization, but the polygons with the mass centers in the triangle nodes. As consequence, considering a medium value among 5 to 8 faces for each polygon, the numeric integration and the system of algebraic equations becomes more extensive and costly. Some authors reportam although, for high numbers of Peclet in convection problems and diffusion, the mistake associated to the gradients is high, generating instabilities in the solution.

Recent researches showed that the triangle can be used directly in the Finite Volume method, unhappily the formulations were deduced for convective problems. For diffusive problems however, the formulations are not still very available in the literature, reason for which I began this context in this forum.

thank you for the contributions,

Marcio Aredes Martins Mechanical Engineering Department Universidade Federal de Minas Gerais - BRAZIL

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