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Sequence: Order of Solving NS Equations

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Old   January 12, 2019, 03:51
Default Sequence: Order of Solving NS Equations
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can anybody give me some hints on literature, youtube videos, websites where it is explained, in which sequence the momentum, mass , energy and ideal gas equation are solved?
So all equations depend on each other, but I would like to see some scheme/programming code for an finite volume code, so for one CELL , and want to see what happens here while calculating all the variables.

All I always see is: explenation fv method + discretisation of one CELL for momentum equation. But what happens to the other equations?

Thank you

Best regards
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Old   January 12, 2019, 07:43
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A better way is to say that equations are coupled.

Coupled solvers solve all the equations at the same time.

Solving equations in any order is a segregated approach and now there is a order to their dependence. SIMPLE is a popular approach to solving the continuity & momentum equation pair. You can just check out simpleFoam or rhoSimpleFoam in OpenFOAM. You'll see that the momentum equation is solved. Then the energy equation. Then the pressure correction equation for SIMPLE.

Originally Posted by CellZone View Post
All I always see is: explenation fv method + discretisation of one CELL for momentum equation. But what happens to the other equations?

I guess you are on the right track. Discretization for other equations happens in similar fashion. No real tricks here if you understand it for the momentum equation. The question is what the approach to solve this set of coupled systems. Discretization schemes don't really matter for learning this part either. You can imagine there is some discretization and some funky equation for one cell, and similar ones for all cells, and this creates a big (linear) system that must be solved. Until you actually code your own code you can ignore the little details surrounding discretization as long as you recognize it must be done at some point.
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