Navier-stokes div U=0 term question

stridder · July 7, 2015, 02:05

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, 04:05

Quote:

Originally Posted by stridder

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, 19:02

Quote:

Originally Posted by FMDenaro

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, 19:17

Section 7.6 in

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

stridder · July 8, 2015, 20:46

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, 21:31

http://link.springer.com/book/10.1007/978-3-642-56026-2

July 7, 2015, 02:05	Navier-stokes div U=0 term question	#1
stridder New Member Join Date: Jul 2015 Posts: 7 Rep Power: 11	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!

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July 8, 2015, 19:17		#4
FMDenaro Senior Member Filippo Maria Denaro Join Date: Jul 2010 Posts: 6,855 Rep Power: 73	Section 7.6 in http://download.springer.com/static/...10f2217c31bef8

July 8, 2015, 20:46		#5
stridder New Member Join Date: Jul 2015 Posts: 7 Rep Power: 11	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."

July 8, 2015, 21:31		#6
FMDenaro Senior Member Filippo Maria Denaro Join Date: Jul 2010 Posts: 6,855 Rep Power: 73	http://link.springer.com/book/10.1007/978-3-642-56026-2