no-slip boundary condition in axi-symmetric flow

[David Pekker]

Hi, 

I am trying to solve the Stokes problem of flow around a sphere (similar to the Gerris calculation in www.lmm.jussieu.fr/~lagree/COURS/M2MHP/petitRe.pdf). 

For small Re (I am using Re=0.1) the pressure on the surface of a unit sphere should be close to the Stokes solution: P=-(3 Cos[\theta])/(2 Re). Running the problem with Gerris I indeed obtain something that looks like the Stokes solution, but using Basilisk (see image) I obtain something quite different.

Interestingly, if instead of defining a boundary I just set the velocities inside the sphere to zero I recover the correct behavior of the pressure on the surface of the sphere using Basilisk.

Any pointers as to what has gone wrong would be greatly appreciated.

Sincerely,

David

[Antoon van Hooft]

Hallo David,

Maybe it is due to inconsistent boundary conditions; Unless you set it explicitly, the sphere will use the default scalar conditions for the pressure ( i.e. neumann(0.)).
You could easily set it the Stokes solution, but that does not seem very attractive.

However, the NS-solver page has a special note on this 'issue':

For the default symmetric boundary conditions, we need to ensure that the normal component of the velocity is zero after projection. This means that, at the boundary, the acceleration a must be balanced by the pressure gradient. Taking care of boundary orientation and staggering of a, this can be written

  p[right] = neumann(a.n[ghost]*fm.n[ghost]/α.n[ghost]);
p[left] = neumann(-a.n[]*fm.n[]/α.n[]);

#if AXI
uf.n[bottom] = 0.;
#else // !AXI
# if dimension > 1
p[top] = neumann(a.n[ghost]*fm.n[ghost]/α.n[ghost]);
p[bottom] = neumann(-a.n[]*fm.n[]/α.n[]);
# endif
# if dimension > 2
p[front] = neumann(a.n[ghost]*fm.n[ghost]/α.n[ghost]);
p[back] = neumann(-a.n[]*fm.n[]/α.n[]);
# endif
#endif

I do not know how this should be extended easily for non-grid-aligned boundaries like the sphere.

Luckily, you already found the solution by not using mask.  

Antoon

[John Dalton]

I have just started learning Basilisk and would like to study the (axisymmetric) stokes flow past a sphere, and then I found this post and example.

The provided code simulates a half sphere, but I would like to see the whole sphere. I am totally puzzled by why I get "Floating point exception (core dumped)" if I change just the origin from 

origin(-L0/2., 0) 

to

origin(-L0/2., -L0/2.) 

Any pointers? anyone?

Best,

John