initial residual and final residual

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 September 5, 2022, 06:19 initial residual and final residual #1 Senior Member   Sangho Ko Join Date: Oct 2021 Location: South Korea Posts: 130 Rep Power: 3 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. https://www.youtube.com/watch?v=OOILoJ1zuiw&t=1s 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? https://youtu.be/OOILoJ1zuiw?t=281 At this link, is representing Navier-Stokes equation. So I've thought 'Ax=b' that Zbynek is referring is meaning Navier-Stokes equation and same to . 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, https://youtu.be/OOILoJ1zuiw?t=360 can be transformed into . And this means can be expressed like below link. https://youtu.be/OOILoJ1zuiw?t=410 Also 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 , how M(same thing to A in 'Ax=b') can be updated? Thank you~!

 Tags pimple, residual, simple algorithm