0
$\begingroup$

Consider a regular rectangular 2D $r$-$z$ mesh with constant spacing $\Delta r$ along the $r$-axis with $n$ points and spacing $\Delta z$ along the $z$-axis with $m$ points. I thought it would be a straightforward formula for node connectivity/node numbering. But searching the internet is finding complicated ideas for general situations.

What is the formula for the node number of the point $(i, j)$ in a regular rectangular 2D $r$-$z$ mesh with constant spacing?

$\endgroup$

1 Answer 1

2
$\begingroup$

Supposing that you enumerate first in $r$ and then in $z$, you have the following enumeration

$$n_\text{node} = j n + i\, ,$$

assuming zero-indexing.

It is a good exercise for you to deduce this result. I think it is correct, but it does not hurt to double-check.

$\endgroup$
3
  • $\begingroup$ Also, it is interesting to think about how different choices for 1D enumeration can make the numerical solution easier or harder. $\endgroup$ Aug 9, 2022 at 18:45
  • $\begingroup$ what are j, n and i? $\endgroup$
    – wander95
    Aug 9, 2022 at 19:49
  • 2
    $\begingroup$ $i$, $j$ and $n$ are defined in your original question. $\endgroup$
    – nicoguaro
    Aug 10, 2022 at 2:34

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.