Impulse density formulation of incompressible Euler's equations.

Outrageous · February 10, 2018, 23:18

Hello, I've been trying to study the impulse density formulation of the incompressible Eulers equations . I have to discretize the following equation (For a zero gauge transformation)

$\partial$ v/ $\partial$ t+ v. $\nabla$ v = 0.

For the lid driven cavity using staggered grid. I'm unable to comprehend certain things , i.e. we have neglected viscosity so how will the vortices be affected?

Here v indicates the two dimensional velocity vector.

FMDenaro · February 11, 2018, 05:35

The lid driven cavity has the driving force trasmitted by the movement of the lid to the fluid, a fact that requires tha action of the viscous stress. Therefore, you cannot solve the Euler flow model.

Outrageous · February 11, 2018, 13:45

Exactly, that's what I was thinking.So if I wanted to solve the NS equations, how to discretize it?(except using the vorticity-stream function transformations) (I want to use zero gauge transformation) . The issue is with non linear convective terms .

FMDenaro · February 11, 2018, 13:52

Quote:

Originally Posted by Outrageous

Exactly, that's what I was thinking.So if I wanted to solve the NS equations, how to discretize it?(except using the vorticity-stream function transformations) (I want to use zero gauge transformation) . The issue is with non linear convective terms .

Why the issue is only in the non linear term? You have also the coupling with the pressure to ensure a divergence-free velocity field.
Use some well known method, for example
http://crd.lbl.gov/assets/pubs_presos/BCMIIJCP.pdf
https://ntrs.nasa.gov/archive/nasa/c...9840014260.pdf

February 10, 2018, 23:18	Impulse density formulation of incompressible Euler's equations.	#1
Outrageous New Member Outy Join Date: Feb 2018 Posts: 12 Rep Power: 8	Hello, I've been trying to study the impulse density formulation of the incompressible Eulers equations . I have to discretize the following equation (For a zero gauge transformation) $\partial$ v/ $\partial$ t+ v. $\nabla$ v = 0. For the lid driven cavity using staggered grid. I'm unable to comprehend certain things , i.e. we have neglected viscosity so how will the vortices be affected? Here v indicates the two dimensional velocity vector.

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February 11, 2018, 05:35		#2
FMDenaro Senior Member Filippo Maria Denaro Join Date: Jul 2010 Posts: 6,897 Rep Power: 73	The lid driven cavity has the driving force trasmitted by the movement of the lid to the fluid, a fact that requires tha action of the viscous stress. Therefore, you cannot solve the Euler flow model.

February 11, 2018, 13:45		#3
Outrageous New Member Outy Join Date: Feb 2018 Posts: 12 Rep Power: 8	Exactly, that's what I was thinking.So if I wanted to solve the NS equations, how to discretize it?(except using the vorticity-stream function transformations) (I want to use zero gauge transformation) . The issue is with non linear convective terms .