ENH: LambVector FO is expensive to compute

Problem statement: LambVector expression is

$(\nabla \times \mathbf{u}) \times \mathbf{u}$

, which revealed to be expensive to compute.

Problem solution: Equivalent expressions, and potential simplifications, e.g. for incompressible flow computations, may reduce the computational cost of LambVector.

Most of the time the divergence of LambVector is the actual field of interest rather than the LambVector itself.

Nevertheless, the divergence of lambVector is computed by an external div FO. Instead,

$\nabla \cdot ((\nabla \times \mathbf{u})\times \mathbf{u})$

may be further reduced to a simpler form.

changed milestone to %v2006

added enhancement label

https://en.wikipedia.org/wiki/Lamb_vector

In addition, the LambVector prints twice per time-step:

functionObjects::lambVector lambVector1 writing field: myLambVector
functionObjects::div div1 writing field: myDivlambVector

functionObjects::lambVector lambVector1 writing field: myLambVector
functionObjects::div div1 writing field: myDivlambVector

changed milestone to %v2012

$$\bm{l} = \bm{\omega} \times \bm{u} = \bm{u}\cdot\nabla\bm{u} - (\bm{u}\cdot\nabla)\bm{u} = \bm{u}\cdot\nabla\bm{u} - 0.5\nabla(\bm{u}\cdot\bm{u})$$

$$\nabla\cdot\bm{l} = (\nabla\times\bm{\omega})\cdot\bm{u} - \bm{\omega}\cdot\bm{\omega}$$

With incompressible approximation (i.e.

$\nabla\cdot\bm{u}=0$

):

$$\nabla\cdot\bm{l} = (-\nabla^2\bm{u})\cdot\bm{u} - \bm{\omega}\cdot\bm{\omega}$$

changed title from WIP: lambVector FO is expensive to compute to ENH: LambVector FO is expensive to compute

changed the description

made the issue visible to everyone

changed milestone to %v2112

closed