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Are separate matrices created for various Navier-Stokes equaions?

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Old   September 2, 2019, 10:14
Default Are separate matrices created for various Navier-Stokes equaions?
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Mandeep Shetty
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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)

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Old   September 2, 2019, 10:51
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Originally Posted by granzer View Post
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.
For example, see here http://www.academia.edu/download/431...20-14mrxrh.pdf
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Old   September 2, 2019, 11:14
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Originally Posted by FMDenaro View Post
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.
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Old   September 2, 2019, 12:27
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@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.

Try this link to download the paper
https://www.google.com/url?sa=t&rct=...u_anzyQ8NiyMQK
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Old   September 2, 2019, 14:31
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Originally Posted by FMDenaro View Post
Try this link to download the paper
https://www.google.com/url?sa=t&rct=...u_anzyQ8NiyMQK
Thank you!
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