Hello,
There is a term that I don’t understand in this webpage on discretization schemes for the Navier-Stokes equations.
See the line
We subtract the equation for
\bf u^\ast from the equation for \bf u^n to obtain [...] = - \nabla(p^{n-1/2}-p^\ast).
The equation for \bf u^n contains p^{n+1/2}, not p^{n-1/2}. So shouldn’t it be [...] = - \nabla(p^{n+1/2}-p^\ast)?
Also, \delta t right before “A common choice […]” should be \Delta t.
Best
The first equation should contain p^{n-1/2} not p^{n+1/2}, thus p^*=p^{n-3/2} would be the common choice.
Please note that issues with the tutorial should rather be addressed at: Sign in to GitHub · GitHub.
Is this because the sentence
We start by selecting a p^\ast such that p^\ast=𝑝^{𝑛+1/2}+𝑂(\delta t)
should be replaced by
We start by selecting a p^\ast such that p^\ast=𝑝^{𝑛-1/2}+𝑂(\delta t)
?
Also, is p^{n-3/2} defined as (p^{n-2}+p^{n-1})/2?
Yes, that would be the idea. I’ve now updated the webpage to reflect this.