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initial residual and final residual

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Old   September 5, 2022, 06:19
Question initial residual and final residual
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Sangho Ko
Join Date: Oct 2021
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Hello everybody~!

I was wondering what is initial residual and final residual.
So I've searched these things in CFD Online and Youtube.
I've seen video at below link.
And I've found this post
SIMPLE: Difference between initial and final residuals

At upper link, 'Zbynek' has said that
"When your final residual is low enough, you update the matrix and repeat the whole process I just described (called outer iteration). Voila, you get a new initial residual that has naturally a larger value than the previous final residual."

I'm wondering two points.

1. Deos 'Ax=b' means Navier-Stokes equation?
At this link, MU=-\triangledown p is representing Navier-Stokes equation. So I've thought 'Ax=b' that Zbynek is referring is meaning Navier-Stokes equation and same to MU=-\triangledown p.
Is it right?

2. If 'Ax=b' means Navier-Stokes equation, then how A can be updated during outer iteration?
What I've guessed is below.
At below link,
MU=-\triangledown p can be transformed into Au-H=-\triangledown p.
And this means H=AU-MU can be expressed like below link.
Also H=AU-MU means H can be changed by U.
Because H is changed by U and H is component of MU, if U is updated M must be changed.
And M is same thing to A in 'Ax=b'
Is it right? I'm not sure...
Eventhough we've updated only x then substitute it into MU=-\triangledown p,
how M(same thing to A in 'Ax=b') can be updated?

Thank you~!
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pimple, residual, simple algorithm

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