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why velocity and pressure are decoupled in incompressible flow? 

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June 10, 2023, 11:34 
why velocity and pressure are decoupled in incompressible flow?

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Why is it said that velocity and pressure are decoupled in incompressible flow? To my understanding, coupling means mutual influence. From the governing equations, pressure and velocity certainly affect each other, so how should we understand the statement "velocity and pressure are decoupled in incompressible flow"?


June 10, 2023, 12:12 

#2 
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In the incompressible limit, there is no thermodynamic pressure. Once you apply the continuity equation and (obtain the density), the pressure is no longer a free variable. The pressure is whatever it needs to be to satisfy continuity. You can interpret this as decoupling or severely constrained coupling.


June 10, 2023, 13:07 

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i understand all your sentences except for the last, i mean: the meaning of "decoupling" and "severely constrained coupling" are antonyms for me.


June 10, 2023, 13:08 

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June 10, 2023, 13:26 

#5 
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I think you should focus first on the fact that the pressure is nothing but a potential function whose gradient generates a velocity that accomodates for the divergencefree constraint. There is no EOS for the pressure.
The system of equation is coupled but the link provided by the mass constraint can be shown to generate a lagrangian multiplier. Then, “decoupling” is a term often used in a numerical formulation, for example in the fractional time step. If you have a specific reference where you read that, post it. 

June 10, 2023, 13:44 

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i read that "velocity and pressure is decoupling in the incompressible flows" in a Chineselanguage textbook, so even i show you, you can't read. so i have two more little question to my confusion 1. do you heard the "velocity and pressure is decoupling in the incompressible flows" before?may be it is not a widely accepted knowledge/saying. 2. may be "velocity and pressure is decoupling in the incompressible flows" is only used in CFD not in theory of fluid mechanics? but it sounds impossible too: How can there be a numerical algorithm where the pressure and velocity evolve separately 

June 10, 2023, 14:30 

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In CFD there is the historical idea of the "splitting" method that can be applied both for the spatial dimensions and for the physical terms in the equations. For example in reacting flows where the reactions are very fast compared to the other terms. In case of incompressible flows, the socalled "pressurefree projection method" produces a sequence of steps for an intermediate velocity, the pressure field and the correction step. 

June 10, 2023, 19:48 

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That remaining p that you solve in the navierstokes isn't the thermodynamic pressure anymore it is just a field that enforces the continuity equation. Whatever is the thing that remains that we label p is severely constrained. If it helps, just change what we label p to another name in the incompressible navier stokes, call it pepperonipizza instead. Presure is decoupled, pepperoni is constrained to be on the pizza. 

June 11, 2023, 23:02 

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June 11, 2023, 23:40 

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June 13, 2023, 11:10 

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Compressible flow may be in dynamic nonequilibrium, but in thermodynamic equilibrium. Thermodynamic equilibrium doesn't mean that the gas properties are not changing in space and time. It only means that for a infinitesimal fluid parcel (chich can contain billions of molecules) I can define meaningful averages of the properties based on the statistics of the molecular behavior.


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cfd, fluid mechanics, incompressible flows 
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