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How to obtain the Jacobian matrix of linearized Navier–Stokes equations

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Old   March 10, 2022, 09:32
Default How to obtain the Jacobian matrix of linearized Navier–Stokes equations
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SUN
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Dear all,
Recently, I am new to the hydrodynamics' linear stability analysis. And I have read a relative literature on linear stability analysis using openFoam(https://www.sciencedirect.com/scienc...00936116300024).
On the framework of openfoam, my question is that how to obtain the Jacobian matrix of the right handside of linearized Navier–Stokes equations as mentioned in equation(6).
All suggestions are appreciated.
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Old   March 16, 2022, 15:13
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Have a look at this. https://www.google.com/url?sa=t&sour...7Buj1hHcIWT3Ze.

There you will find the Jacobian matrix of the linear navier stokes equation
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Old   March 18, 2022, 07:39
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OpenFoam does *not* apply a Newton iteration to linearize the non-linear convective terms in the momentum equation.

OpenFoam instead employs a successive iteration (fixed point iteration, Picard iteration instead, see wiki for explanation of these terms). See openfoam documentation.

OpenFoam does not compute a Jacobian.

Examples of public domain codes that do maybe compute the Jacobian include Fenics, FireDrake, NGSolve, Gridap, Ferrite, WaterLilly and Trixie.
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flow instability, icofoam, linearized navier–stokes

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