# Are separate matrices created for various Navier-Stokes equaions?

 Register Blogs Members List Search Today's Posts Mark Forums Read

 September 2, 2019, 10:14 Are separate matrices created for various Navier-Stokes equaions? #1 Senior Member   Mandeep Shetty Join Date: Apr 2016 Posts: 179 Rep Power: 8 CFD is based on governing equations, which are generally continuity equation, momentum equations, and/maybe energy equation (consider all of them together as Navier-Stokes equations). All these 3 equations (let's consider the 3 momentum equations as one), after discretizing gives a system of linear equations. My question is, are there separate matrices created for each of these equations or is there just one, sort-of a global matrix created using info from all three questions? (I am a beginner and am learning discretizing and solution of single PDEs like heat equation but have not studied coupled PDEs like NS equation) Last edited by granzer; September 2, 2019 at 23:41.

September 2, 2019, 10:51
#2
Senior Member

Filippo Maria Denaro
Join Date: Jul 2010
Posts: 6,041
Rep Power: 64
Quote:
 Originally Posted by granzer CFD is based on governing equations, which are generally continuity equation, momentum equations, and/maybe energy equation (consider all of them together as Navier-Stokes equations). All these 3 equations (let's consider the 3 momentum equations as one), after discretizing gives a system of linear equations. My question is, are there separate matrices created for each of these equations or is there just one, sort-of a global matrix created contacting info from all three questions? (I am a beginner and am learning discretizing and solution of single PDEs like heat equation but have not studied coupled PDEs like NS equation)

The system is not linear even after the discretization, you have to see as a single matrix.

September 2, 2019, 11:14
#3
Senior Member

Mandeep Shetty
Join Date: Apr 2016
Posts: 179
Rep Power: 8
Quote:
 Originally Posted by FMDenaro The system is not linear even after the discretization, you have to see as a single matrix. For example, see here http://www.academia.edu/download/431...20-14mrxrh.pdf
@FMDenaro: When you say 'you have to see as a single matrix' do you mean the 3 equations made into a separate matrice? Is this to facilitate linearization?. There is a problem loading the page.

September 2, 2019, 12:27
#4
Senior Member

Filippo Maria Denaro
Join Date: Jul 2010
Posts: 6,041
Rep Power: 64
Quote:
 Originally Posted by granzer @FMDenaro: When you say 'you have to see as a single matrix' do you mean the 3 equations made into a separate matrice? Is this to facilitate linearization?. There is a problem loading the page.

September 2, 2019, 14:31
#5
Senior Member

Mandeep Shetty
Join Date: Apr 2016
Posts: 179
Rep Power: 8
Quote:
Thank you!

 Tags navier stoke solver