I'm still curious as to your opinions, if any, on the questions below.

Cheers,

Kristján

On Wed, Aug 11, 2010 at 2:44 PM, Kristjan Gudmundsson <kristjang@gmail.com> wrote:

Hi Stephane,

In the Physalis method we use the the Stokes equations to transform

the no-slip boundary condition on the sphere to a surrounding

grid-conforming 'cage' of nodes. The presence of the sphere is then

communicated to the bulk flow via the extrapolated BC on the cage. So,

the task of getting Physalis to work in Gerris has two major

components:

a) Determine the coefficients in Lamb's solution to Stokes equation on

a sphere and then evaluate the expansion on the cage. This has less to

do with Gerris and more with the Physalis idea.

b) Let Gerris know about the cage and the velocity of the points comprising it.

It seems I could define the cage as a solid and then do something like

"GfsSurfaceBc U/V/W Dirichlet VALUE_FROM_PHYSALIS". I have two

questions relating to this:

1) Are cells inside solids removed from the flow field? If so then the

cage will have to be inside the sphere (as opposed to

straddling/intersecting the spherical surface), increasing the error a

bit.

2) Gerris' discretization is 1st order near solid interfaces since

face gradients are not calculated at the center at partial faces. This

would mean the calculation near my cage is 1st order, partially

defeating the purpose of the exercise. However, it seems that 2nd

order accuracy will prevail if the cage is constructed as the union of

cell-interfaces, eliminating partial faces. Is this true?

Hope you're enjoying Paris!

Kristján

--

Kristján Guđmundsson, Ph.D.

Physics of Fluids Group

Applied Physics Dept., Uni. of Twente

www.its.caltech.edu/~kristjan

--

Kristján Guđmundsson, Ph.D.

Physics of Fluids Group

Applied Physics Dept., Uni. of Twente

www.its.caltech.edu/~kristjan