Creating a mesh within spherical shell with gmsh 4.7.1 - mesh

Question

I'm trying to use gmsh 4.7.1 to create a mesh within a 3D volume, that is a sphere with a concentric spherical hole (in other words, I have a spherical shell). In order to do so, I wrote the following .geo file:
// Gmsh project created on Wed Feb 17 15:22:45 2021
SetFactory("OpenCASCADE");
//+
Sphere(1) = {0, 0, 0, 0.1, -Pi/2, Pi/2, 2*Pi};
//+
Sphere(2) = {0, 0, 0, 1, -Pi/2, Pi/2, 2*Pi};
//+
Surface Loop(3) = {2};
//+
Surface Loop(4) = {1};
//+
Volume(3) = {3, 4};
//+
Physical Surface(1) = {1};
//+
Physical Surface(2) = {2};
//+
Physical Volume(3) = {3};
But, as soon as I create a 3D mesh by using the 3D command in the gmsh gui, my inner hole gets meshed too, while I'd like to have no elements of the mesh within the hole.
What am I doing wrong? How can I obtain the desired result? Thank you.

Answer 1

There are several issues at play here:
Sphere command, already creates a volume, not surfaces as you expect.
due to the point above, the command Surface Loop(3) = {2}; is assumed to create a surface loop from a volume, which is 1) not a supported operation. 2) will try to use the surface with the tag 2. It is unclear, what it will do in reality (as a surface with the tag 2 probably still exists).
Thus, the Volume command gets some weird things as an input
and it is all connected with the fact that the characteristic length is not setup, thus the mesh density is quite arbitrary.
If you insist on using the OpenCASCADE kernel, you probably want to use boolean operations.
Here is the code I have with an arbitrarily chosen characteristic length of 0.05 for all the points defining the solid spherical shell:
SetFactory("OpenCASCADE");
Sphere(1) = {0, 0, 0, 0.1, -Pi/2, Pi/2, 2*Pi};
Sphere(2) = {0, 0, 0, 1, -Pi/2, Pi/2, 2*Pi};
BooleanDifference(3) = { Volume{2}; Delete; }{ Volume{1}; Delete; };
Characteristic Length{ PointsOf{ Volume{3}; } } = 0.05;
Visualization from Paraview of the produced mesh with clipping: