Navier–Stokes equations

Questions
1

Hi!

How to write general form of Navier–Stokes equations?

2

This blog is a good start:

Using Mathematica to Simulate and Visualize Fluid Flow in a Box

It fully solves 2D problem of one moving boundary

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and gets nice vertex flows:

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There are detailed descriptions of proper equations and numerical discretization. You can generalize to 3D. I would look also in latest V10 functionality to see if anything can be used there to upgrade the methods of the blog - it was written before V10 came out. For instance, take a look at this Stokes Flow example which is a simplification of NS:

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