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I am about to start my journey into the world of CFD and wanted to start with the Fractional-step method for solving the incompressible Navier-Stokes equations. Could you perhaps suggest some articles or books I should look into (for this method specifically)?

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  • $\begingroup$ I tagged it (as displayed under), among other tags, as operator-splitting. Was that sensible ? $\endgroup$ – imranal Jun 6 '13 at 12:59
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Check out

An overview of projection methods for incompressible flows;
Guermond, Minev, Shen;
Comput. Methods Appl. Mech. Engrg., 195 (2006);
http://www.math.ust.hk/~mawang/teaching/math532/guermond-shen-2006.pdf

It gives a fairly good overview over a bunch of solver classes, amongst others the fractional-step methods such as pressure-correction (e.g., the Chorin's classical method). It also talks a bit about the difficulty in chosing boundary conditions (especially for the pressure).

For a more detailed overview, I found the book

Finite Element Methods for Flow Problems; Jean Donea, Antonio Huerta; http://books.google.de/books/about/Finite_Element_Methods_for_Flow_Problems.html?id=S4URqrTtSXoC&redir_esc=y

quite helpful.

For the practical implementation, I'd recommend looking into FEniCS. The FEniCS book, https://bitbucket.org/fenics-project/fenics-book/downloads/fenics-book-2011-10-27-final.pdf, also has a chapter (III-21) devoted to comparing all sorts of different methods for incompressible Navier-Stokes.

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  • $\begingroup$ I am coincidentally also learning FEniCS, so that will be my next goal; to implement a Navier-Stokes solver using FEniCS. $\endgroup$ – imranal May 8 '13 at 19:31
  • $\begingroup$ Then you should definitely check out launchpad.net/nsbench. This is the code base for said book chapter. $\endgroup$ – Nico Schlömer May 8 '13 at 19:33
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An improved discussion of issues related to boundary conditions for pressure and stability of projection methods for the incompressible Navier-Stokes equations is in this paper:

J.-G. Liu, J. Liu, R.L. Pego, Stable and accurate pressure approximation for unsteady incompressible viscous flow, J. Comp. Phys. 229 (2010) 3428-3453.

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