Hi, I am solving NS equations and trying to code them in Matlab for lid driven cavity.
I have solved the problem using FDM but I have very little experience with FVM.
Can anyone help me with the discretization
Please let us know more about the problem. What kind of solver are you using? Are you using staggered or collocated grid system?
Hi Tanmay,
Thanks for your reply. I am using collocated grid and primitive variable formulation. The issue is when I am trying to solve this problem for very High Reynolds no, I need to have very fine mesh around the boundaries.
I solved the problem using Finite difference but if I refine my mesh around the boundaries, I will have to perform grid transformation. And if I refine the mesh throughout the domain, it increases the computational time .
Also my ultimate objective is to solve flow field around a cylinder and an airfoil , for which I will be using FVM.
I would like to start from learning how to discretize transient 2D momentum equation for non-uniform rectangular grid
Thanks Tiago,
I will defintely go through Patankar's book and try to develop an understanding of FVM.
Why deny the use of calculus and vector field theory in formulating an arbitrary discretization? A Galerkin weak form in the continuum sets the stage, thereafter selecting a FE trial space basis embeds all the coordinate data, with the final step being conversion to a recursive "stencil". Optimal MODIFIED CONTINUOUS Gelerkin CFD, Wiley 2014, provides complete details.
Hi A.J. Baker,
Thanks for your reply
I dont have access to this book at present but do you have any code ( preferably matlab) to solve any simplistic CFD problem using FEA formulation?
FINITE ELEMENTS - Computational Engineering Sciences, Wiley 2012, fully details FEA methodology at an introductory level including CFD. Visit the supporting website to download a Matlab toolbox specifically designed to implement FEA algorithms.
I can recommand you differents books. If you don't have a lot of experience with Finite Volume Method. th first book you must have from my point of view (simple and easy to understand) is :
Computational Fluid Dynamics: Principles and Applications, 3rd Edition
Jiri Blazek
2015, Butterworth-Heinemann
the companion website contains the sources of 1-D and 2-D Euler and Navier-Stokes flow solvers (structured and unstructured) and other tools ...
see below
http://booksite.elsevier.com/9780080999951/
An other interesting book you can download from this adress :
https://ekaoktariyantonugroho.files.wordpress.com/2008/04/an-introduction-to-computational-fluid-dynamics-versteeg.pdf
As mentioned before, Patankar Book is a very good place to start. TEACH-2E Code is developed based on it . You Can learn more by looking at the code.
Dear Shashank, I have used FEM in Mathematica for lid driven cavity with good results (see images in .doc file). For a use of Scilab (= Matlab), see the attached paper by Margonari. Gianluca
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