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Vector Field Formulation of the Helmholtz decomposition

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Old   August 23, 2024, 16:20
Default Vector Field Formulation of the Helmholtz decomposition
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M Shaaban
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I am trying to apply a Helmholtz decomposition to separate compressible and noncompressible components of a velocity field.

https://arc.aiaa.org/doi/10.2514/1.J058836

I successfully managed to do the scalar potential formulation in OpenFOAM. It's so simple but has shortcomings on concave domains.

I am trying to implement the following problem:

Capture.GIF

Using vector identities, I can convert the curl-of-curl equation to a fvm formulation.

What about these funcy BCs? They specify the curl of the unknown vector field Av. What can I do about these?
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boundary condition, curl, decomposition


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