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-   -   Navier-stokes div U=0 term question (https://www.cfd-online.com/Forums/main/156263-navier-stokes-div-u-0-term-question.html)

stridder July 7, 2015 01:05
Navier-stokes div U=0 term question
 
Hello,

I have found the following sentence somewhere on internet about Navier-Stokes:
"Velocity and pressure are coupled via constraint div U=0 for which pressure is the Langrange multiplier."
I work on numerical simulation of a model described by incompressible time-dependent Navier-Stokes equations.
Can smbd help me to understand why velocity and pressure are coupled in this term?
how is it related to Langrange multiplier?
Does the coupling need special attention when solving linear system that comes from weak formulation of Navier-Stokes if I use linear approximation to nonlinear term in Navier-Stokes equation, for example Crank-Nicolson method?
Thank you!

FMDenaro July 7, 2015 03:05
Quote:
Originally Posted by stridder (Post 554076)
Hello,

I have found the following sentence somewhere on internet about Navier-Stokes:
"Velocity and pressure are coupled via constraint div U=0 for which pressure is the Langrange multiplier."
I work on numerical simulation of a model described by incompressible time-dependent Navier-Stokes equations.
Can smbd help me to understand why velocity and pressure are coupled in this term?
how is it related to Langrange multiplier?
Does the coupling need special attention when solving linear system that comes from weak formulation of Navier-Stokes if I use linear approximation to nonlinear term in Navier-Stokes equation, for example Crank-Nicolson method?
Thank you!


Hello, you cand find the answer in the book of Peric & Ferziger. There is a dedicated section

stridder July 8, 2015 18:02
Quote:
Originally Posted by FMDenaro (Post 554098)
Hello, you cand find the answer in the book of Peric & Ferziger. There is a dedicated section
Could you please specify the name of the book?
Thanks

FMDenaro July 8, 2015 18:17
Section 7.6 in

http://download.springer.com/static/...10f2217c31bef8

stridder July 8, 2015 19:46
something is wrong with the link.
"Page not found

Sorry, the page you requested is unavailable. The link you requested might be broken, or no longer exist."

FMDenaro July 8, 2015 20:31
http://link.springer.com/book/10.1007/978-3-642-56026-2


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