How to solve fluid flow problem based on Navier-Stokes equations?

Does anyone know or can provide any examples how fluid flow problem can be formulated and solved in Wolfram Language? Simplest cases of 1D or 2D flows based on Navier-Stokes equations or even their linearized version would be great to see.

Replay

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

How to solve fluid flow problem based on Navier-Stokes equations?

and gets nice vertex flows:

How to solve fluid flow problem based on Navier-Stokes equations?

How to solve fluid flow problem based on Navier-Stokes equations?

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:

How to solve fluid flow problem based on Navier-Stokes equations?

The same example is discussed in Solving Partial Differential Equations with Finite Elements tutorial

How to solve fluid flow problem based on Navier-Stokes equations?

that goes a bit further and solves for pressure and other quantities:

How to solve fluid flow problem based on Navier-Stokes equations?

Category: differential equations Time: 2014-08-15 Views: 0

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