Issue on page /chapter2/ns_code2.html

[mcastel1]

The natural boundary condition for the Poisson-like equation for \phi cannot be satisfied, it is satisfied only to within $O(\Delta t)$, see https://fenicsproject.discourse.group/t/natural-boundary-condition-is-not-satisfied/16606/8?u=mekong .

This should be clarified in the webpage.

[jorgensd]

I don't think it needs to be added. This tutorial does not have the goal of analysing the complete splitting scheme.
This is the job of: https://computationalphysiology.github.io/oasisx/splitting_schemes.html
where there also are references to several theoretical papers on the proposed method.

You can also find the improved method where one keep an extra term in the equation:


(the term that is dropped in this tutorial).
In the Navier stokes eq this becomes:

Please also note that this is an open source project. If you have a good way of formulating what you want to have on the web-page, you can simply modify the source code and add a pull request.

[mcastel1]

Do as you wish, but a boundary condition whose residual is huge in the first few steps, and stays large in the following, needs a comment, to the very least. This was confusing not only to me, but also to another colleague of mine.

[jorgensd]

Do as you wish, but a boundary condition whose residual is huge in the first few steps, and stays large in the following, needs a comment, to the very least. This was confusing not only to me, but also to another colleague of mine.

In general, when starting with a zero flow as initial condition, one sees these kind of «spikes» in the pressure/phi, as p_old is 0. This is not unique to this splitting scheme.