Steady-state solver

[cibinj...@gmail.com]

Hi,

I'm trying to understand how the wake deformation works for the quasi-steady solver in VSPAero. I understand a flat-wake is first initialized and then the wake collocation points are updated to match the streamline.

For a local velocity V = (u, v, w), and the streamline parameter s, the differential equation being solved for is

dx/ds = u/|V| 

dy/ds = v/|V|

dz/ds = w/|V|

In the discretized form (for say the x-component) this becomes,

x_{i+1} = x_{i} + u/|V| * (s_{i+1} - s_{i})

This seems to be what VSPAero is also doing with an additional relaxation factor.

I'm unable to understand how this results in a converged solution. I do not see how all of (u, v, w) will reduce to zero, since there will always be induced velocity from nearby vortices.

I'm sure I'm missing something!

Any help/hints are appreciated.

Thanks!

Cibin

[Rob McDonald]

The x{i+1} here is the next x along a given wake -- not the updated position of the same x at the next timestep.

So, u,v,w do not have to go to zero for this to converge.  Instead, the wake line needs to lie parallel to the local velocities along a streamline.

That said, it does not converge.  Notice that even with many wake iterations, the residuals do not drop to zero.  They come down, but then they stop.  For simple cases, they don't really improve all that much compared to a fixed wake.

Lift and Drag do a pretty good job of converging, but the wake points wiggle around forever.

Dave is actually working on a mode that will address this for other reasons -- it won't be ready for release for quite some time (I have to get the huge release before that one done first).  It is a good bit slower, but it provides much more formal convergence behavior to the wake.

Rob

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[Cibin Joseph]

Oh, I see! I kept interpreting it as a fixed-point iteration.

Now it makes sense.

Looking forward to seeing what Dave comes up with next!

Thanks Rob!

Cibin

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[Brandon Hicks]

Is progress on this being made? I find that the convergence vs number of wake iterations is very oscillatory, and residuals almost never decrease much beyond the 2nd or 3rd iteration. 

Brandon Hicks